Physics I: Week One - RQ and HW
What does the Greek letter delta (Δ) mean?
A change in something
The units of acceleration are ___________.
m/s/s or m/s²
The motion diagram for something slowing down would look like...
Dots that get closer together
Velocity vectors point...
In the same direction as displacement vectors
Making rough estimates of physical quantities is useful....
So that you can see if the answer to a problem makes physical sense
A dog trots from -11 m to 7 m in 17 s. What is its velocity?
*velocity (vector quantity) has both magnitude and direction; is the rate of change of displacement of an object V = ∆x/∆t V = velocity ∆x = change in position or displacement ∆t = time interval *x₁ = -11 m x₂ = 7 m ∆t = 17 s displacement is , ∆x = x₂-x₁ = (7 m)-(-11 m) = 18 m velocity (v) = ∆x/∆t v = 18m/17s = 1.1 m/s
Which of the following is an example of uniform motion?
1) A hockey puck sliding in a straight line at a constant speed. 2) A ball dropped from the top of a building. 3) A car going around a circular track. 4) A person speeds up while running in a straight line. *if object has acceleration, cannot be an example of uniform motion; uniform motion must be in a straight line
Keira starts at position x = 29 m along a coordinate axis. She then undergoes a displacement of -48 m. What is her final position?
x = -19 m *Negative displacement = displacement in an opposite direction. Net displacement of Keira is, x = 29 + (-48) = 29-48 = x = -19 m, her final position
Jeni walks 100 meters east and then 50 meters north. How big is Jeni's displacement from the starting point?
About 112 m
It takes Harry 42 s to walk from x₁ = -10 m to x₂= -50 m. What is his velocity?
Harry's velocity is -0.95 m/s V = x₂-x₁/∆t = (-50 m) - (-10 m)/42 s = -0.95 m/s
What is the difference between speed and velocity?
Velocity contains information about the direction of motion while speed does not. *speed is a scalar quantity; contains magnitude *velocity is a vector quantity; contains magnitude and direction. *speed is the rate of change of distance with respect to time *velocity is the rate of change of displacement with respect to time.
A motorist is traveling at 20 m/s. He is 60 m from a stop light when he sees it turn yellow. His reaction time, before stepping on the brake, is 0.50 s. Choose a motion diagram showing the motorist's position and his velocity vectors.
1) The reaction time of the motorist is 0.5 sec. During this time interval, he is moving with uniform velocity and covers equal distance in equal time intervals. 2) After 0.5 s the breaks are working and decreasing the velocity. Now the distance covered in equal time intervals is also decreasing. 3) Known values: Initial speed of the motorist v = 20 m/s His distance from the stop light x = 60 m Reaction time t = 0.5 s 4) The motorist travels with a speed 'v' till he is at a distance x from the stoplight and after 0.5 s he applies brakes. The motorist then travels with constant deceleration 'a' before coming to a stop.
If you throw a ball against the ceiling—so the ball moves upward and then rebounds to move downward—at the instant the ball hits the ceiling, the acceleration is?
Negative
Determine the sign (positive or negative) of the position and the velocity for the motion diagram in (Figure 1)?
Negative position, positive velocity
The slope at a point on a position-versus-time graph of an object is the __________.
Object's instantaneous velocity at that point *The slope of a position time graph is, slope = ∆x/∆t This is the change in position to change in time which gives the velocity. At a given instant, the slope will give the velocity at that instant.
If Sam walks 100 m to the right, then 200 m to the left, his net displacement vector is..
Points to the left
In a typical greyhound race, a dog accelerates to a speed of 20 m/s over a distance of 30 m. It then maintains this speed.
*Given that in a greyhound race the dog accelerates at a speed of 20 m/s till the distance 30 m. While accelerating, the position and velocity of the graph will increase. After that the dog moves with constant velocity with equally spaced position in time. This is continued till 100m.
A car travels to the left at a steady speed for a few seconds, then brakes for a stop sign. Select the correct motion diagram of the car for the entire motion described here. The dots are numbered in order, starting with zero.
(A) → Initially, the car is moving with uniform (constant) speed for a few seconds; spacing between the dots must be the same. → After applying the breaks, the car comes to a rest; spacing between dots decreases
You are standing on a straight stretch of road and watching the motion of a bicycle; you choose your position as the origin. At one instant, the position of the bicycle is negative and its velocity is positive. Is the bicycle getting closer to you or farther away? Explain.
If the position of the bicycle is negative it is to your left. The bicycle's velocity is positive, or to the right, so the bicycle is getting closer to you. *the bicycle is located at the negative side (your left) and is moving in a positive direction (to your right) closer to you
The area under a velocity-versus-time graph of an object is?
The displacement of the object. *V = displacement/time or, displacement = velocity x time or, displacement = area. *since the area under the curve is the product of velocity and time with some constant factor (depends on nature of the curve)
(Figure 1) shows the motion diagram for a horse galloping in one direction along a straight path. Not every dot is labeled, but the dots are at equally spaced instants of time. A. What is the horse's velocity during the first 10 seconds of its gallop? B. What is the horse's velocity during the interval from the 30s to 40s? C. What is the horse's velocity during the interval from 50s to 70s?
A: Velocity during first 10 seconds Displacement/time = x₂-x₁/t₂-t₁ = 500-600/10-0 = - 10 m/s B: Velocity during 30s-40s interval x₂-x₁/t₂-t₁ = 300-350/40-30 = -5 m/s C: Velocity during 50s-70s interval x₂-x₁/t₂-t₁ = 50-250/70-50 = -10 m/s
The figure shows an object's position-versus-time graph. (Figure 1) (A) What is the velocity of the object at 6 s ? (B) What is the initial position of the object?
A. 3.3 m/s B. 5.00 m
Part A: Suppose you are hiking along a trail. Make a comparison between the magnitude of your displacement and your distance traveled. Part B: Suppose a runner completes one lap around a 400-m track in a time of 50 s. Calculate the magnitude of the average velocity of the runner. Part C: Suppose a runner completes one lap around a 400-m track in a time of 50 s. Calculate the average speed of the runner. Part D: Consulting the graph shown in (Figure 1), determine the object's average velocity over the time interval from 2 to 4 seconds.
A: * The magnitude of the displacement is always less than or equal to the distance traveled along any path. → The magnitude of your displacement can be less than your distance traveled. → The magnitude of your displacement can be equal to your distance traveled. B: The displacement of the runner is zero because after one lap the runner is at its initial position. Thus, the average velocity is V = displacement/time taken = 0 m/50 s = 0 m/s C: The average speed is Distance traveled/time taken = 400 m/50 s = 8 m/s D. Average velocity = total displacement/total time So, Xf - Xi/Tf - Ti = 20 - 10/4 - 2 =10/2 = 5 m/s * Average velocity of a graph is the slope of the straight line connecting the endpoints of a curve
(Figure 1) shows Sue along the straight-line path between her home and the cinema. A. What is Sue's position x if her home is the origin? Assume the positive direction is to the right. B. What is Sue's position x if the cinema is the origin? Assume the positive direction is to the right.
A: If Sue's home is the origin; since Sue's position is to the right of her house = positive direction x = +2 m B: If cinema is the origin; since Sue's position is to the left of the cinema = negative direction x = -3 m
If a car has a negative displacement, what does that indicate?
*Displacement is a vector quantity; has a magnitude (size) and a direction car has moved in the negative direction (moving in the opposite direction/backwards)
Brian leaves Los Angeles at 8:00 a.m. to drive to San Francisco, 400 mi away. He travels at a steady 50 mph . Sarah leaves Los Angeles at 9:00 a.m. and drives a steady 60 mph. (A) Who gets to San Francisco first? (B) How long does the first to arrive have to wait for the second?
d = 400 mi v (Brian) = 50 mph v (Sarah) = 60 mph A. Sarah t (Brian) = d/v (Brian) = 400/50 = 8 hrs t (Sarah) = d/ v (Sarah) = 400/60 = 6.67 hrs t (Brian) > t (Sarah) B. 19.8 min (8-1)-6.67 = 0.33 hrs = 19.8 min
A softball player hits the ball and starts running toward first base. Select a correct motion diagram, showing her velocity vectors during the first few seconds of her run.
*Since the softball player starts running after hitting the ball, the initial velocity of the player was low and it increases as she moves towards the base
A skydiver jumps out of an airplane. Her speed steadily increases until she deploys her parachute, at which point her speed quickly decreases. She subsequently falls to earth at a constant rate, stopping when she lands on the ground.
*The initial velocity is zero. The velocity increases and the space between the position markers increases until the chute is deployed. Once the chute is deployed, the velocity decreases and the spacing between the position markers decreases until a constant velocity is obtained. Once a constant velocity is obtained, the position markers are evenly spaced.
A child is sledding on a smooth, level patch of snow. She encounters a rocky patch and slows to a stop. Select a correct motion diagram, showing her velocity vectors.
*The length of each arrow represents the average speed of the child. The average speed of the child is the same until the sled encounters a rocky patch. During this time, the acceleration of the child is zero. After encountering a rocky patch the average speed of the sled decreases rapidly with time. So, the child has negative acceleration and the sled comes to a complete stop.
A car skids to a halt to avoid hitting an object in the road. Select the correct motion diagram of the car from the time the skid begins until the instant the car stops.
*When brakes are applied, the velocity of the car decreases as time passes (the car deaccelerates until its velocity becomes zero). The distance between each time interval will decrease.
Which of the following motions is described by the motion diagram of the figure? (Figure 1)
A) An ice skater gliding across the ice. B) An airplane braking to a stop after landing. C) A car pulling away from a stop sign. D) A pool ball bouncing off a cushion and reversing direction. *The distance between adjacent position markers increase along the progress of motion. Hence, the object is covering greater distances across equal time intervals as the motion progresses (its velocity is increasing with time or the object is accelerating).
Which of the following motions could be described by the motion diagram of the (Figure 1) ?
A) hockey puck sliding across smooth ice. B) A cyclist braking to a stop. C) A sprinter starting a race. D) A ball bouncing off a wall. *The cyclists position is decreasing from right to left; so, the object is coming to rest, its velocity gradually decreases.
