02_Kinematics 1 & 2 Dimensions
displacement
(1) "the change in position" (2) how far an object is from its starting point. (3) it is a vector (meaning direction maters)
What is true of an object thrown upwards if air resistance is negligible?
(1) At it's highest point, Velocity = 0 (2) the time to get highest point equals the time to return to the start. [At half the total time of travel the object is at its highest point (3) It will return to it's original position with the same speed that it was initially thrown with
How do you solve relative motion problems?
(1) Identify each type of motion and it's frame of reference. Label each with a two letter subscript abbreviation( first letter is object; 2nd letter frame of reference) (2) Identify direction of each type of motion (3) Solve by adding, subtracting, triangle or summation.
dynamics
(1) the study of the causes of motion.(force, mass and energy) (2) the study of why objects move(Force, Mass & Energy)
what are the three methods of adding vectors and there pseudonyms?
(1) triangle method (aka tail-to-tip method aka head to tail method)(2) parallelogram method (3) Component method
kinematics
(1)the study of motion without regard to it's cause. (2) the study of how objects move
QQ 2.2 True or False? Define east as the negative direction and west as the positive direction. (a) If a car is traveling east, its acceleration must be eastward. (b) If a car is slowing down, its acceleration may be positive. (c) An object with constant non zero acceleration can never stop and stay stopped. Explain
(a) False (b) True (c) True. it can have non zero acceleration and stop, but it can't stay stopped.
CQ 11 Explain whether the following particle do or do not have an acceleration: (a) a particle moving in a straight line with constant speed and (b) a particle moving around a curve with constant speed
(a) No (b)Yes, moving around the curve changes direction
A ball is thrown upward in the air by a passenger on a train that is moving with constant velocity. (a) Describe the path of the ball as seen by the passenger. Describe the path as seen by a stationary observer outside the train. (b) How would these observations change if the train were accelerating along the track?
(a) The passenger see is the object move straight up and down while the stationary observer sees the ball move in a parabolic fashion. (b) Both would describe the path as parabolic.
QQ3.5 Consider the following controls in a car: gas pedal, brake, steering wheel. The controls in this list that cause an acceleration of the car are (a) all three controls; (b) the gas pedal and the brake, (c) only the brake, or (d) only the gas pedal.
(a) all three controls
True or False|| If an object has an acceleration of 2m/s/s upwards, In space it would have an acceleration of 10m/s/s in space?
...
Kinematic equations
5 equations
Parallelogram method usage reminders
A graphical method of adding two vectors where each vector is drawn from the same origin and a parallelogram is constructed with the adjacent sides. Then a resultant is drawn diagonally from the common origin . -this can only be used to add two vectors.
meet problem
A kinematic physics problem where objects travelling from opposite directions eventually meet or arrive after some traveled distance. the total distance traveled equals the sum of the distance traveled by each.
CQ 14. A ball is projected horizontally from the top of a building. One second later, another ball is projected horizontally from the same point with the same velocity. At what point in the motion will the balls be closest to each other? Will the first ball always be traveling faster than the second? What will be the time difference between them when the balls hit the ground? Can the horizontal projection velocity of the second ball be changed so that the balls arrive at the ground at the same time?
The point initially is when the second ball is closest to the first. Yes, the first ball will always be traveling faster than the 2nd. The time difference between each hitting the ground is 1 second. No change in initial horizontal velocity will allow the second ball to reach the ground before the first. If you could change the initial horizontal speed, we may have an argument, but definitely not the horizontal.
(a) How do I know what's positive and negative in my Kinematic Equation? (b) what's default? (c) how do I change this for my purposes
This will depend on your coordinate system and what you define as positive. you must realize that the unspoken default coordinate system is ground Level is 0 and up/right is positive. It doesn't have to be this way though When defining a coordinate system there are two things you must. (1) Identify your origin (2) Indicate with an arrow which direction is positive
calculating displacements when distances are given instead of displacements
To calculate displacement in one-dimensional motion[either x-or-y direction] you subtract the final position from the initial position. However, if multiple displacements are given instead of positions you add the displacements [with respect to their directions] and the result is your displacement. If the displacements have. x & y components or both you add them in t each dimension & use Pythagorean theorem & inverse tangent to find the resultant displacement..
True or False When an object falls the net acceleration is equal to gravity?
True. Even when the object is thrown upwards first and then falls its acceleration is equal to gravity at all points
what does forwards and backwards mean in one dimensional kinematics?
forward refers to movement East ( to the right on the x-axis movement) backwards means movement West (to the left on the x-axis movement)
Define uniformly accelerated motion what conditions are true when this is SO?
situation where the magnitude of the acceleration is constant for an object moving in a straight line. (1) average acceleration = instantaneous acceleration (2) If acceleration is constant(does not change), then average velocity is the midpoint[average] of the initial and final velocities
how do you solve for instantaneous velocity?
solve for v.
speed & velocity
speed [1] how fast something goes. [2] how far something moves in a certain amount of time; velocity [1] the change in position over time; [2] how fast and in what direction does an object move; [3] displacement over time;
resultant vector
the vector sum of two or more vectors the vector resulting from the addition of two or more vectors.; the vector resulting from the addition of vectors
projectile motion
two dimensional motion; motion where objects move in the x[horizontal] & y[vertical] direction simultaneously[at the same time]. Are you familiar with Galileo? He was the first to describe projectile motion accurately. He showed that it could be understood by analyzing the horizontal & vertical components of the motion separately.
average speed vs. average velocity
usually these two terms will have the same magnitude but sometimes they will not because average speed is the total distance traveled in a certain amount of time while average velocity is the total displacement traveled in a certain amount of time; another difference is that average velocity factors in direction while average speed doesn't. The difference between these two terms only occurs rarely and doesn't really need to be discussed.
CQ9. As a projectile moves in its path, is there any point along the path where the velocity and acceleration vectors are (a) perpendicular to each other (b) parallel to each other?
(a) at the peak of the projectiles path where the y component of velocity is zero (b) only If the projectile is thrown straight up or down. During this situation it will be parallel during all points of the motion. For any other kind of projectile motion, the velocity and acceleration vectors are never parallel.
*QQ 2.8 A skydiver jumps out of a hovering helicopter. A few seconds later, another skydiver jumps out so they both fall with the same acceleration. Does the vertical distance between them (a) increase, (b) decrease or (c) stay the same? Does the difference in their velocities (d) increase, (e) decrease, or (f) stay the same? (Assume the g is constant.) Explain
(a) vertical distance increases. Because the first diver left earlier, He will always travel faster during his second than the second diver. Since he's traveling faster per second he travels further too. (f) stays the same because the acceleration, change in velocity is constant
*CQ 12 A rule of thumb for driving is that a separation of one car length for each 10 mph of speed should be maintained between moving vehicles. Assuming a constant reaction time, discuss the relevance of this rule for (a) motion with constant velocity and (b) motion with constant acceleration
(a)For objects moving with constant velocity this rule of thumb is true (b) however objects that move with constant acceleration experience continuous change in their velocity which means that the distance between cars will be changing as well.
QQ 3.4 Which of the following objects cannot be accelerating? (a) AN object moving with constant speed; (b) an object moving with constant velocity; (c) an object moving along a curve.
(b) an object moving with a constant velocity. (a) is wrong because you can change the direction and still travel at constant speed. the changing direction causes the acceleration change (c) is wrong because direction changes and possible speed changes when moving along a curve.
QQ3.7 As a projectile moves in its parabolic path, the velocity and acceleration vectors are perpendicular to each other (a) everywhere along the projectile's path, (b) at the peak of its path, (c) nowhere along it's path or (d) not enough information is given
(b) at the peak of its path.
QQ3.6 Suppose you are carrying a ball and running at constant speed, and wish to throw the ball and catch it as it comes back down. Should you (a) throw the ball at an angle of 45 degrees above the horizontal and maintain the same speed, (b) throw the ball straight up in the air and slow down to catch it, or (c) throw the ball straight up in the air and maintain the same speed?
(c) throw the ball straight up and maintain the same speed.
QQ 2.7 A tennis player on serve tosses a ball straight up. As the tennis ball travels through the air, its speed (a) increases (b) decreases (c) increases and then decreases, (d) decreases and then increases, or (e) remain constant? Explain
(d) it decrease and then increases
QQ 2.6 A tennis player on serve tosses a ball straight up. While the ball is in free fall, does it's acceleration (a) increase (b) decrease (c) increase and then decrease, (d) decrease and then increase, or (e) remain constant? Explain
(e) remain constant... unless the ball is equipped with a motor or wings it has no ability to change it's acceleration. The acceleration the object will experience is that of gravitational acceleration.
catch problem
A kinematic physics problem where one object catches or surpasses another when traveling in the same direction. either the distance traveled be each object will be equal so that x1 = x2. or if an object never catches or surpasses then x1 = x2 ± lead/lag distance the time needed to catch is equal (t1 = t2) unless one object starts before or after t1 = t2 ± lead/lag time.
Component method usage reminders
A method for adding vectors by breaking each vector into its x and y components, summing the vectors in each component, then using Pythagorean theorem and tangent to determine the resultant vector.
Galileo's free fall
A situation where an object moves (falls) only under the influence of gravity. Even if an object is thrown up or down it is said to be in free fall since gravity is the only force acting on it.
CQ 19 You drop a ball from a window on an upper floor of a building. The ball strikes the ground with speed V. You now repeat the drop, but you have a friend down on the street who throws another ball upward at speed v. Your friend throws the ball upward at exactly the same time that you drop yours from the window. At some location the balls pass each other. Is this location at the halfway point between window and ground, above that point, or below that point?
Above the halfway point. The thrown pebble has an initial velocity and travels further than the dropped pebble which has no initial velocity. As a result the thrown pebble travel further.
vector
Any quantity that has both magnitude and direction.(ex displacement, velocity, acceleration)
scalar
Any quantity that has only magnitude but no direction(ex. mass, temperature
Displacement vs. Distance
Displacement is the change in position; how far an object is from where it started; Distance is how far an objects travels; Example: A person travels 10 miles right and two miles left. Displacement would be 8 miles and Distance would be 12
True or False An object that is thrown upward and has an initial speed has some sort of initial acceleration?
False...The only way the object with an initial velocity would have an initial acceleration other than that of gravity is if the object has some sort of ability to change it's velocity (like an engine or wings or some external source of acceleration, like air resistance)
True or False When an object rises the acceleration it has is greater in magnitude to both frictional force and gravity.
False..the acceleration is the same at all points. Witch is equal to gravity.
You travel from point A to point B in a car moving at a constant speed of 70km/h. Then you travel the same distance from point B to another point C. moving at a constant speed of 90 km/h. ls your average speed for the entire trip from A to C equal to 80 km/h? Explain why or why not.
In this instance, you cannot calculate average speed this way. You can only do this if you know that acceleration is constant during the interval. In this problem speed is constant but acceleration is not. [show them v versus t with linear slope and another v versus t with flat, linear slope, flat.]
CQ 13Two cars are moving in the same direction in parallel lanes along a highway. At some instant, the velocity of car A exceeds the velocity of car B. Does this mean that the acceleration of A is greater than that of B? Explain
No. Car B may be picking up speed (that is, accelerating and have a higher acceleration) but have not reached the speed of car A yet. there are many other possible scenarios
CQ6. Can a vector have a component greater than its magnitude A?
No.. the x and y component of a vector is cosine or sine of the angle times the vector. The maximum value for cos and sin is 1 and therefore the component values will never exceed value of vector.
Does positive acceleration and the word "accelerate" mean the same thing?
Not always Positive acceleration means the object[whether it's accelerating or decelerating] has an acceleration pointing in the positive direction[according to the frame of reference.] If an object is moving faster[accelerating] in the positive direction It's acceleration is positive. IF an object is moving faster[accelerating] in the negative direction. It's acceleration is negative, despite the fact the object is accelerating.
Does negative acceleration and decelerate mean the same thing?
Not always. Negative acceleration is when acceleration points in the negative direction. Deceleration is when an object is slowing down or decreasing in speed. If an object is moving forward and then begins to slow down, it is decelerating and the acceleration vector is negative. Let's say the speed a car traveling 60m/s travels at 50m/s after one second. The acceleration has a negative value of -10m/s/s. If an object is moving in the negative direction at -40 m/s and then slows down to -30 m/s, the car decelerated[slowed down] but the deceleration is positive.
If an object is slowing down does that mean that it's acceleration is negative?
Not necessarily. If an object moves in the direction deemed positive and then slows down, then yes deceleration will be negative. However if an object is moving in a direction deemed negative and then slows down the deceleration will have a value that is positive.
CQ 7 A child throws a marble into the air with an initial speed Vo. Another child drops a ball at the same instant. Compare the accelerations of the two objects while they are in flight.
Once the objects leave the hand, they both have the same acceleration equal in magnitude to g gravity.
What three things are true about an object thrown upwards during free-fall or projectile motion?
The [vertical component] of velocity at the highest point is zero[because the object is not moving. The acceleration at all points equals gravity. The time it takes to reach the highest point equals half the total time. The initial[vertical component of the] speed of the ball equals final[vertical component] speed.
How do you break a vector into its x & y components?
The hardest part of breaking a vector into its x & y components is when to use sine & cosine. It all depends on what axis the angle is measured from. If the angle is measured from the x-axis you will use cosine for x and sine for y. If the angle is measured from the y you will use sine for x and cosine for y.
CQ10. A rock is dropped at the same instant that a ball is thrown horizontally from the same initial elevation. Which will have the greater speed when it reached ground level?
The rock that is thrown horizontally will have a greater speed . The rock thrown has an initial velocity where the dropped rock does not. While there y component of velocity will be the thrown rock will have an additional x-component that factors in to the total velocity
CQ 13. A spacecraft drifts through space at a constant velocity. Suddenly, a gas leak in the side of the spacecraft causes it to constantly accelerate in a direction perpendicular to the initial velocity. The orientation of the spacecraft does not change, so the acceleration remains perpendicular to the original direction of the velocity. What is the shape of the path followed by the spacecraft?
The spacecraft will follow a parabolic path equivalent to that of a projectile thrown off a cliff with a horizontal velocity. In regards to the projectile, gravity provides an acceleration that is always perpendicular to the initial( and constant) velocity. this is analogous to the leaking rocket ship. why is the path not a straight sloped line... For the path to be straight and sloped the velocity and perpendicular velocity due to the leak needs to be constant. While the velocity is constant, the velocity due to the leak is not because its causing it to accelerate, therefore creating a parabolic path and a non straight sloped line.
Why would a train that leaves 4 seconds later than another train be represented as (t-4)?
The train has to wait 4 seconds before it can leave. After one second has the train left the station? No. after two seconds has the train left? No. After three seconds has the train left? No. After 5 seconds has the train left? Yes. How long has the train be traveling for? 1 second. (t-4)
mechanics
the study of the motion of objects, force and energy. mechanics is usually divided into two parts. kinematics and dynamics; the study of how and why object move.
CQ 15 A student at the top of a building of height h throws one ball upward with a speed of Vo and then throws a second ball downward with the same initial speed, Vo. How do the final velocities compare when the balls reach the ground?
The velocities will be the same. It will take the first ball longer to reach the ground but when it hits the ground it will have the same velocity.
how do we define the reference frame?
The view from which you judge the motion of another object In every day life we tend to define the frame of reference with respect to Earth. We assign up or north as the positive y-axis & east & right or East to the positive x-axis.
What are the components of relative motion? how do you orientate yourself for a problem like this
There are always three components of relative motion for any object: i) motion of object 1 with respect to earth; ii) motion of object 2 with respect to earth; iii) motion of object 1 to object 2 To orientate your self consider two cars traveling in the same direction (from faster cars perspective and slower cars perspective) and two cars traveling in opposite directions
CQ2 If vector B is added to vector A, under what conditions does the resultant vector have a magnitude equal to A + B? Under what conditions is the resultant vector equal to zero?
When vector A and B are pointed in the same direction. The implication here is that "A + B" are scalars. When vector A and B point in opposite directions and the are equal in magnitude.
translational motion
[1] movement of an object in a straight line. [2] movement of an object that excludes rotation or vibration.
acceleration
[1] the change in velocity over time. [2] a measure of how much the velocity changes in a certain amount of time.
Triangle method usage reminders
a graphical method of adding vectors where the first vector is drawn and each additional vector starts at the tip (where the last vector ended) of the previous vector. When all vectors have been drawn a resultant vector is drawn from tail of the first vector to the tip of the last vector. - triangle method obeys the commutative law of addition. This means that the order in which the vectors are added doesn't matter the resultant vector will be the same - this method can be used to add more than two vectors. Some other methods cannot. - if only two vectors are added the result looks like a triangle. If more than two it doesn't
frame of reference
the choice of coordinate axes that defines the starting point, [positive] direction of motion & whether the starting point is stationary or moving. the choice of a starting point, direction, and relativity[fixed or moving] of motion. [2] the choice of a starting point & direction[s] of motion to be positive [ & negative].
Define decelerate||How does this term relate to positive and negative acceleration?
the slowing down of an object; the loss of speed/velocity of an object; an object whose speed or velocity decreases. deceleration occurs when the object velocity & acceleration vectors point in opposite directions Deceleration is negative when an object moves in the positive direction and slows down. Deceleration is positive when an object moves in the negative direction and slows down. Regardless of direction, deceleration is always defined as the object slowing down.