Physics Study Guide

The average speed of an object which moves 10 kilometers (km) in 30 minutes is ____. a. 10 km/hr b. 20 km/hr c. 30 km/hr d. more than 30 km/hr

Answer: B The average speed is distance/time. In this case the distance is 10 km and the time is 0.5 hr (30 minutes). Thus average speed = (10 km)/(0.5 hr) =20 km/hr

The phrase "30 mi/hr, west" likely refers to a scalar quantity.

FALSE - The presence of the direction "west" in this expression rules it out as a speed expression. Speed is a scalar quantity and direction is not a part of it.

Both speed and velocity refer to how fast an object is moving.

FALSE - Speed refers to how fast an object is moving; but velocity refers to the rate at which one's motion puts an object away from its original position. A person can move very fast (and thus have a large speed); but if every other step leads in opposite directions, then that person would not have a large velocity.

If an object is at rest, then the position-time graph will be a horizontal line located on the time-axis.

FALSE - Not necessarily true. If the object is at rest, then the line on a p-t graph will indeed be horizontal. However, it will not necessarily be located upon the time axis.

Position-time graphs cannot be used to represent the motion of objects with accelerated motion.

FALSE - Position-time graphs represent accelerated motion by curved lines.

Acceleration is a vector quantity.

TRUE - Yes it is. Acceleration is direction-conscious.

A fullback is running down the football field in a straight line. He starts at the 0-yard line at 0 seconds. At 1 second, he is on the 10-yard line; at 2 seconds, he is on the 20-yard line; at 3 seconds, he is on the 30-yard line; and at 4 seconds, he is on the 40-yard line. What is the player's acceleration?

Answer: 0 m/s/s The fullback is moving 10 yards every second. He has a constant speed. He also is running in a straight line, so he is not changing direction. Thus, his acceleration is 0 m/s/s. Only objects with changing velocity have a nonzero acceleration.

The quantity 9.8 m/s/s is an acceleration value and as such is a vector quantity.

FALSE (a rather picky FALSE) - If a direction was included, then this would be an acceleration value. The unit is characteristic of acceleration but the lack of direction is inconsistent with acceleration being a vector quantity.

Accelerated objects are represented on position-time graphs by curved lines.

TRUE - Accelerating objects (if the acceleration is attributable to a speed change) are represented by lines with changing slope - i.e., curved lines.

An object which is slowing down has an acceleration.

TRUE - Accelerating objects are either slowing down, speeding up or changing directions.

If an object is at rest, then the velocity-time graph will be a line with zero slope.

TRUE - An object that is at rest has a 0 velocity and maintains that zero velocity. The permanence of its velocity (not the fact that it is zero) gives the object a zero acceleration. and as such, the line on a v-t graph would have a slope of 0 (i.e., be horizontal).

A person makes a round-trip journey, finishing where she started. The displacement for the trip is 0 and the distance is some nonzero value.

TRUE - Displacement is the change in position of an object. An object which finishes where it started is not displaced; it is at the same place as it started and as such has a zero displacement. On the other hand, the distance is the amount of ground which is covered. And if it was truly a journey, then there is definitely a distance.

The average velocity of an object on a round-trip journey would be 0.

TRUE - For a round trip journey, there is no ultimate change in position. As such, the average velocity is 0 m/t seconds. Regardless of the time, the average velocity will be 0 m/s.

A straight, diagonal line on a position-time graph is representative of an object with a constant velocity.

TRUE - A straight diagonal line is a line of constant slope. And if the slope is constant, then so is the velocity.

The value of g on Earth is approximately 9.8 m/s2.

TRUE - Yes! Know this one!

An object with a negative acceleration will be represented on a position-time graph by a line which curves downwards.

FALSE - (Once more, there is confusing wording here since we might not all agree on what "curving downwards" means.) A line that slopes downwards and has a curve (perhaps you call that "curving downwards " as I do) has a negative velocity (due to its negative slope). If the curve is "concave up" (you might say leveling off to a horizontal as time progresses) then the object is slowing down and the acceleration is positive.

An object with a positive acceleration will be represented on a position-time graph by a line which curves upwards.

FALSE - (This is confusing wording here since we might not all agree on what "curving up" means.) A line that slopes upward and has a curve (perhaps you call that "curving up" as I do) has a positive velocity (due to its positive slope). If the curve is "concave down" (you might say leveling off to a horizontal as time progresses) then the object is slowing down and the acceleration is negative.

A line with zero slope on a velocity-time graph will be representative of an object which is at rest.

FALSE - A line with zero slope is representative of an object with an acceleration of 0. It could be at rest or it could be moving at a constant velocity.

A line with a negative slope on a velocity-time graph is representative of an object with negative velocity.

FALSE - A negative slope indicates a negative acceleration. The object could be moving in the positive direction and slowing down (a negative acceleration).

An object that is accelerating is moving fast.

FALSE - Accelerating objects are not necessarily moving fast; they are merely changing how fast they are moving (or the direction they are moving).

Accelerating objects MUST be changing their velocity.

TRUE - Accelerating object MUST be changing their velocity -either the magnitude or the direction of the velocity.

For any given motion, it is possible that an object could move very fast yet have an abnormally small velocity.

TRUE - An Indy Race car driver is a good example of this. Such a driver is obviously moving very fast but by the end of the race the average velocity is essentially 0 m/s.

Which one of the following statements is NOT true of a free-falling object? An object in a state of free fall ____. a. falls with a constant speed of -10 m/s. b. falls with a acceleration of -10 m/s/s. c. falls under the sole influence of gravity. d. falls with downward acceleration which has a constant magnitude.

Answer: A A free-falling object is an object upon which the only force is gravity. As it falls, it accelerates at a rate of approx. 10 m/s/s. This acceleration value is constant during the entire trajectory of the motion. Since this is the case, the speed can not be constant.

As an object freely falls, its ____. a. speed increases b. acceleration increases c. both of these d. none of these

Answer: A As an object falls, it accelerates; this means that the speed will be changing. While falling, the speed increases by 10 m/s every second. The acceleration is a constant value of 10 m/s/s; thus, choice b should not be chosen.

What is the acceleration of a car that maintains a constant velocity of 55 mi/hr for 10.0 seconds? a. 0 b. 5.5 mi /hr/s c. 5.5 mi /s/s d. 550 mi/hr/s

Answer: A If the velocity is constant, then there is no acceleration. That is, the value of the acceleration is 0.

If an object is moving eastward and slowing down, then the direction of its velocity vector is ____. a. eastward b. westward c. neither d. not enough info to tell

Answer: A The direction of the velocity vector is always in the same direction as the direction which the object moves.

If an object is moving eastward and slowing down, then the direction of its acceleration vector is ____. a. eastward b. westward c. neither d. not enough info to tell

Answer: B If an object is slowing down, then the direction of the acceleration vector is in the opposite direction as the direction which the object moves. (If the object were speeding up, the acceleration would be eastward.)

Consider drops of water that leak from a dripping faucet at a constant rate. As the drops fall they ____. a. get closer together b. get farther apart c. remain at a relatively fixed distance from one another

Answer: B Since the drops of water are falling (and probably free-falling), they should be getting farther apart as they fall. This is because the free-falling drops are accelerating and thus gaining speed.

A speedometer is placed upon a free-falling object in order to measure its instantaneous speed during the course of its fall. Its speed reading (neglecting air resistance) would increase each second by ____. a. about 5 m/s b. about 10 m/s c. about 15 m/s d. a variable amounte. depends on its initial speed.

Answer: B The acceleration of gravity is approximately 10 m/s/s. Acceleration represents the rate at which the velocity changes - in this case, the velocity changes by 10 m/s every second. So the speed will increase by the amount of 10 m/s every second.

When a rock is dropped, it will accelerate downward at a rate of 9.8 m/s2. If the same rock is thrown downward (instead of being dropped from rest), it acceleration will be ____. (Ignore air resistance effects.) a. less than 9.8 m/s2 b. 9.8 m/s2 c. more than 9.8 m/s2

Answer: B Whether rising or falling, if the sole force acting upon the object is gravity, then the acceleration is 9.8 m/s/s (often approximated as 10 m/s/s).

Which one of the following quantities is NOT a speed? a. 10 mi/hr b. 10 mi/hr/sec c. 35 m/s d. 20 m/s

Answer: B You can often tell a quantity by its units. 10 mi/hr/sec is an acceleration since there are two time units involved. In fact, the units are velocity change units (mi/hr) per time units (seconds). The quantity speed has units of distance/time.

A baseball pitcher delivers a fast ball. During the throw, the speed of the ball increases from 0 to 30.0 m/s over a time of 0.100 seconds. The average acceleration of the baseball is ____ m/s2. a. 3.00 b. 30.0 c. 300. d. 3000 e. none of these

Answer: C Acceleration is velocity change over time. In this problem, the velocity change is +30.0 m/s and the time is 0.100 s. Thus, a = (+30.0 m/s)/(0.100 s) =300. m/s/s.

Which one of the following is NOT consistent with a car which is accelerating? a. A car is moving with an increasing speed. b. A car is moving with a decreasing speed. c. A car is moving with a high speed. d. A car is changing direction.

Answer: C An accelerating object must be changing its velocity by either slowing down, speeding up or changing direction. Moving fast merely means that the velocity is high; it says nothing about the acceleration.

Ten seconds after being dropped from rest, a free-falling object will be moving with a speed of ____. a. about 10 m/s. b. about 50 m/s. c. about 100 m/s. d. more than 100 m/s.

Answer: C Since the speed of a free-falling object increases by 10 m/s every second, the speed after ten of these seconds will be 100 m/s. You could use the kinematic equation vf= vi+ a*t where vi=0 m/s and a = -10 m/s/s and t=10 s

A fullback is running down the football field in a straight line. He starts at the 0-yard line at 0 seconds. At 1 second, he is on the 10-yard line; at 2 seconds, he is on the 20-yard line; at 3 seconds, he is on the 30-yard line; and at 4 seconds, he is on the 40-yard line. This is evidence that a. he is accelerating b. he is covering a greater distance in each consecutive second. c. he is moving with a constant speed (on average).

Answer: C The fullback is moving 10 yards every second. He has a constant speed and thus covers the same distance (10 yd) in each consecutive second. He is not accelerating.

If an object has an acceleration of 0 m/s2, then one can be sure that the object is not ____. a. moving b. changing position c. changing velocity

Answer: C The object could be moving and could be at rest; however, whether moving or not, it must not have a changing velocity.

On takeoff, a rocket accelerates from rest at a rate of 50.0 m/s2 for exactly 1 minute. The rocket's speed after this minute of steady acceleration will be ____ m/s. a. 50.0 b. 500. c. 3.00 x 103 d. 3.60 x 103 e. none of these

Answer: C Use the equation vf= vi+ a*t vf = 0 + (50.0 m/s/s)*(60.0 s) = 3.00 x 103 m/s (Note that the unit on time must be the same as the time units for which the acceleration is given.)

Which one of the following quantities is NOT a vector? a. 10 mi/hr, east b. 10 mi/hr/sec, west c. 35 m/s, north d. 20 m/s

Answer: D A vector has both magnitude and direction. Only choice d does not show a direction; it must be a scalar.

If car A passes car B, then car A must be ____. a. accelerating. b. accelerating at a greater rate than car B. c. moving faster than car B and accelerating more than car B. d. moving faster than car B, but not necessarily accelerating.

Answer: D All that is necessary is that car A has a greater speed (is moving faster). If so, it will eventually catch up and pass car B. Acceleration is not necessary to overcome car B; a car going 60 mi/hr at a constant speed will eventually pass a car going 50 mi/hr at a constant speed. Surely you have witnessed that while driving down a local highway.

Olympic gold medalist Michael Johnson runs one time around the track - 400 meters - in 38 seconds. What is his displacement? What is his average velocity?

Answer: d = 0 m and v = 0 m/s Michael finishes where he started, so he is not "out of place." His displacement is 0 meters. Since average velocity is displacement over time, his average velocity is also 0 m/s.

Accelerating objects MUST be changing their speed.

FALSE - Accelerating objects could be changing their speed; but it is also possible that an accelerating object is only changing its direction while maintaining a constant speed. The race car drivers at Indy might fit into this category (at least for certain periods of the race).

If an object changes its direction, then the line on the velocity-time graph will have a changing slope.

FALSE - An object which changes its direction will be represented by a line on a v-t graph that crosses over the time-axis from the + velocity region into the - velocity region.

An accelerated object's motion will be represented by a curved line on a velocity-time graph.

FALSE - An object which has an acceleration will be represented by an line that has a slope. It may or may not curve, but it must have a slope other than zero.

An object which is slowing down is represented by a line on a velocity-time graph which is moving in the downward direction.

FALSE - An object which is slowing down has a velocity which is approaching 0 m/s. And as such, on a v-t graph, the line must be approaching the v=0 m/s axis.

Objects with positive acceleration will be represented by upwardly-curved lines on a velocity-time graph.

FALSE - An object with positive acceleration will have an positive or upward slope on a v-t graph. It does not have to be a curved line. A curved line indicates an object that is accelerating at a changing rate of acceleration.

A ball is thrown upwards and is rising towards its peak. As it rises upwards, it is NOT considered to be in a state of free fall.

FALSE - Any object - whether rising, falling or moving horizontally and vertically simultaneously - can be in a state of free fall if the only force acting upon it is the force of gravity. Such objects are known as projectiles and often begin their motion while rising upwards.

A scalar quantity has a magnitude and a vector quantity does not.

FALSE - Both scalar and vector quantities have a magnitude or value expressed with a given unit; additionally, a vector quantity requires a direction in order to fully express the quantity.

The phrase "20 mi, northwest" likely describes the distance for a motion.

FALSE - Distance is a scalar and is ignorant of direction. The "northwest" on this quantity would lead one to believe that this is a displacement (a vector quantity) rather than a distance.

Distance is a vector quantity and displacement is a scalar quantity.

FALSE - Distance is the scalar and displacement is the vector. Know this one!

An object that is moving rightward has a rightward acceleration.

FALSE - If an object is moving rightward and slowing down, then it would have a leftward acceleration.

An object that is moving upwards and slowing down has an upwards acceleration.

FALSE - If an object is slowing down, then the acceleration vector is directed opposite the direction of the motion; in this case the acceleration is directed downwards.

An object that is accelerating will eventually (if given enough time) be moving fast.

FALSE - If the accelerating object is slowing down, then it will eventually stop and not reach a fast speed. And if that doesn't convince you, then consider an object that is accelerating by moving in a circle at constant speed forever; it will accelerate the entire time but never being going any faster than at the beginning.

The symbol g stands for the force of gravity.

FALSE - Nope. A careful physics teacher will never call g the force of gravity. g is known as the acceleration of gravity. It might be best to call it the acceleration caused by gravity. When it comes to the force of gravity, we have yet another symbol for that - Fgrav. But that's a topic to be discussed in a later unit.

Person X moves from location A to location B in 5 seconds. Person Y moves between the same two locations in 10 seconds. Person Y is moving with twice the speed as person X.

FALSE - Person Y has one-half the speed of Person X. If person Y requires twice the time to do the same distance, then person Y is moving half as fast.

A falling skydiver which has reached terminal velocity is considered to be in a state of free fall.

FALSE - Skydivers which are falling at terminal velocity are acted upon by large amounts of air resistance. They are experiencing more forces than the force of gravity. As such, they are NOT free-falling.

A ball is thrown upwards, rises to its peak and eventually falls back to the original height. As the ball rises, its acceleration is upwards; as it falls, its acceleration is downwards.

FALSE - The acceleration of all free-falling objects is directed downwards. A rising object slows down due to the downward gravity force. An upward-moving object which is slowing down is said to have a downwards acceleration.

The direction of the velocity vector is dependent upon two factors: the direction the object is moving and whether the object is speeding up or slowing down.

FALSE - The direction of the velocity vector depends only upon the direction that the object is moving. A westward moving object has a westward velocity.

The slope on a position-time graph is representative of the acceleration of the object.

FALSE - The slope of a position-time graph is the velocity of the object. Some things in this unit are critical things to remember and internalize; this is one of them.

The quantity 20 m/s, north is a speed and as such is a scalar quantity.

FALSE - This is certainly not a speed quantity; though the unit is appropriate for speed, the statement of the direction is inconsistent with speed as a scalar quantity.

A vector is a large quantity and a scalar is a small quantity.

FALSE - This would never be the case. Vectors simply are direction-conscious, path-independent quantities which depend solely upon the initial and final state of an object. Vectors are always expressed fully by use of a magnitude and a direction.

A person starts at position A and finishes at position B. The distance for the trip is the length of the segment measured from A to B.

FALSE - This would only be the case if the person walk along a beeline path from A to B. But if the person makes a turn and veers left, then right and then ..., then the person has a distance which is greater than the length of the path from A to B. Distance refers to the amount of ground which is covered.

A scalar quantity depends only upon the initial and final values of the quantity; this is not the case for vector quantities.

FALSE - Vectors are the types of quantities which depend only upon initial and final state of the object. For instance, the vector quantity displacement depends only upon the starting and final location.

If a person walks in a straight line and never changes direction, then the distance and the displacement will have exactly the same magnitude.

TRUE - If a person never changes direction and maintains the same heading away from the initial position, then every step contributes to a change in position in the same original direction. A 1 m step will increase the displacement (read as out of place-ness) by 1 meter and contribute one more meter to the total distance which is walked.

An object that is moving rightward and speeding up has a rightward acceleration.

TRUE - If an object is speeding up, then the direction of the acceleration vector is in the direction which the object is moving.

A ball is thrown upwards, rises to its peak and eventually falls back to the original height. The speed at which it is launched equals the speed at which it lands. (Assume negligible air resistance.)

TRUE - If the object is truly in free-fall, then the speed of the object will be the same at all heights - whether its on the upward portion of its trajectory or the downwards portion of its trajectory. For more information, see the Projectiles page at The Physics Classroom.

The slope on a velocity-time graph is representative of the acceleration of the object.

TRUE - Now this is important! It is the beginning point of much of our discussion of velocity-time graphs. The slope equals the acceleration.

Scalar quantities are path dependent quantities and vector quantities are not.

TRUE - Scalars such as distance would depend upon the path taken from initial to final location. If you run around the track one complete time, your distance will be different than if you take a step forward and a step backwards. The path MATTERS; distance (like all scalars) depends upon it. On the other hand, the displacement (a vector quantity) is the same for both paths.

An object with a negative velocity will be represented on a position-time graph by a line with a negative slope.

TRUE - Since slope on a p-t graph represents the velocity, a negative slope will represent a negative velocity.

An object with a positive velocity will be represented on a position-time graph by a line with a positive slope.

TRUE - Since slope on a p-t graph represents the velocity, a positive slope will represent a positive velocity.

A very massive object will free fall at the same rate of acceleration as a less massive object.

TRUE - The acceleration of free-falling objects (referred to as the acceleration of gravity) is independent of mass. On Earth, the value is 9.8 m/s/s (the direction is down). All objects - very massive and less massive - experience this acceleration value.

An object in free fall experiences an acceleration which is independent of the mass of the object.

TRUE - The unique feature of free-falling objects is that the mass of the object does not effect the trajectory characteristics. The acceleration, velocity, displacement, etc. is independent of the mass of the object.

The phrase "20 m, west" likely describes the displacement for a motion.

TRUE - The unit is an appropriate displacement unit (length units) and the direction is stated. Since there is both magnitude and direction expressed, one would believe that this is likely a displacement.

The area on a velocity-time graph is representative of the change in position of the object.

TRUE - This is equally important. The area is the displacement.

The direction of the acceleration vector is dependent upon two factors: the direction the object is moving and whether the object is speeding up or slowing down.

TRUE - This is the case and something important to remember. Consider its application in the last three parts of this question.

Acceleration is the rate at which the velocity changes.

TRUE - This is the very definition of acceleration. Know this one - its the beginning point of all our thoughts about acceleration.

An object which is moving at constant speed in a circle has an acceleration.

TRUE - To move in a circle is to change one's direction. As such, there is a change in the velocity (not magnitude, but the direction part); this constitutes an acceleration.

A vector quantity is described with a direction and a scalar is not.

TRUE - Vectors are fully described by magnitude AND direction; scalars are not described with a direction.

Velocity is a vector quantity and speed is a scalar quantity.

TRUE - Yes! Speed is a scalar and velocity is the vector. Know this one!

The velocity of an object refers to the rate at which the object's position changes.

TRUE - Yes! That is exactly the definition of velocity - the rate at which velocity changes.

An object that is free-falling is acted upon by the force of gravity alone.

TRUE - Yes! This is the definition of free fall.