Motion in 1-Dimension
AP Physics C (mechanics)
AP objectives:
Graphing Motion
(Assume the particle starts from the reference frame for all of the graphs that are not x vs. t graphs)
Given the following x vs. t graphs for a particle traveling in a straight line, sketch the v vs. t and a vs. t graphs.
1. x
2. x
t
3. x
t
4. x
t
t
5.
Given the following v vs. t graphs for a particle traveling in a straight line, sketch the x vs. t and a vs. t graphs.
6. v
7. v
t
8. v
9. v
t
t
t
Given the following graphs for a particle traveling in a straight line, sketch the other two quantities.
10.a
11. v
t
12. a
t
13. x
t
t
Motion in 1-Dimension
AP Physics C (mechanics)
14. Calculate the instantaneous velocity of
the particle given the following graph below
for sections A through E.
15. (a) Calculate the acceleration of the car in each
interval: 0 to 4 s, 4 to 8 s, and 8 to 12 s.
(b) Calculate the distance traveled by the car in
each interval: 0 to 4 s, 4 to 8 s, and 8 to 12 s.
16. (a) Calculate the instantaneous velocity of the
particle given the following graph at 25 s.
(b) Calculate the average velocity of the particle
from 0 to 25 s.
(c) During which time interval does the particle
have a constant negative velocity?
17. (a) Calculate the acceleration of the particle at
3.5 seconds.
(b) Calculate the total displacement of the particle
from 0 to 7 seconds.
(c) What can be said about the acceleration during
the 7s to 8 s time interval?
Motion in 1-Dimension
AP Physics C (mechanics)
Motion Equations
1. An electron is accelerated through a cathode ray tube in a TV from rest at a rate of 8.78 x 10 14 m/s2.
The length of the cathode ray tube is 0.4 m. Calculate the velocity of the electron when it strikes the TV
screen.
2. There is a new roller coaster in Abu Dhabi called the Formula Rossa, made by Ferrari. The cars
accelerate from rest to 240 km/h in 4.9 seconds. Assume the acceleration is uniform. (a) Calculate the
acceleration of the roller coaster and (b) the distance traveled during this time.
3. How long would it take a car, starting from rest and accelerating uniformly in a straight line at 5.0 m/s 2,
to cover a distance of 270 meters?
4. How long would it take a car, starting from 10 m/s and accelerating uniformly in a straight line at 5.0
m/s2, to cover a distance of 270 meters?
5. A car that’s initially traveling at 25 m/s slows down uniformly over 8.0 seconds. At the end of 8.0
seconds, the car is traveling at a speed of 19 m/s. (a) Calculate the acceleration of the car. (b) Calculate
the distance traveled by the car during the 8 seconds.
6. Train #1 starts out at position x0 heading in the +x direction at a constant velocity v. Train #2 starts out
at a position d away from x0 heading in the opposite direction towards train #1 with a constant velocity
of 4v. In terms of the variables given, at what time, t, do the trains collide? In terms of the variables
given, at what position, x, do the trains collide?
7. A car initially traveling at a speed v accelerates to a speed of 5v in a time interval t. In that time
interval, the car traveled a distance d. (a) Express the average velocity in terms of v only. (b) Express
the acceleration in terms of v and t only. (c) Express the time elapsed in terms of d and v only. (d)
Express the acceleration in terms of v and d only.
Free Fall
8. A rock is dropped off a cliff and strikes the ground with an impact speed of 31.0 m/s. How high was the
cliff?
9. A person steps off the Golden Gate Bridge and falls into the water below in approximately 3.7 seconds.
(a) How high is the bridge above the water? (b) With what speed does the person strike the water
below?
10. A baseball is fouled off a baseball bat and goes straight up into the air. The ball leaves the bat with an
initial speed of 26.0 m/s. (a) Calculate the maximum height reached by the baseball. (b) Calculate how
long the baseball was in the air before striking the ground.
11. A person is standing on top of a 32.0 meter building and drops one stone off the building, while at the
same time, another stone is thrown down at 6.0 m/s. How much time elapses from the time the first
stone strikes the ground to the second?
12. You are standing on top of the roof of the school which is 11.0 m above the ground. You throw your
physics book straight up into the air at 8.00 m/s, and your friend throws her physics book straight
down at 8.00 m/s. (a) Calculate the time for each to strike the ground below. (b) Calculate the impact
velocities when each book strikes the ground.
13. A rock is thrown up into the air at a velocity v and reaches a maximum vertical distance h. (a) Express
the height h in terms of v and g only. (b) In terms of h, how much higher will the rock travel if it is
thrown up at a speed of 3v?
Motion in 1-Dimension
AP Physics C (mechanics)
Calculus based motion
14. The position of an object as a function of time is given by x = At2 – Bt + C, where A = 8.0 m/s2, B = 6.0
m/s, and C = 4.0 m. Find the instantaneous velocity and acceleration as functions of time.
15. The position of a certain particle depends on time according to the equation x(t) = t2 – 5.0t + 1.0, where
x is in meters if t is in seconds. (a) Determine the expressions for the particle’s velocity and acceleration
as functions of time. (b) Determine the particle’s velocity and acceleration at 3 seconds.
16. The position of a particle along the x axis depends on the time according to the equation x(t) = At 2 – Bt3
where x is in meters and t is in seconds. (a) What SI units must A and B have? For the following, , let
their numerical values in SI units be 3 and 1 respectively. (b) At what time does the particle reach its
maximum positive x position? (c) What is the displacement of the particle at 4 seconds? (d)What is the
instantaneous velocity of the particle at 4 seconds? (e) When does the particle have zero acceleration?
(f) When does the particle have a maximum acceleration?
17. A particle undergoes an acceleration that is non-uniform and varies with time according to
the equation a(t) = (3 m/s3)t
(a) Determine the general expression for the particle’s instantaneous velocity as a function of time.
(b) If the particle’s velocity at t=1 s is v=9 m/s, then determine the particle’s velocity at 3 seconds.
18. Consider a bungee jumper. The motion that results from the pull of the bungee can be modeled by the
following function: v = −5 t3 + 22 t2 − 9.8 t − 20, where v = velocity in m/s and t = time in s. This
equation is valid only for a certain interval of time starting at the instant the bungee first starts to pull
the falling person. (a) Determine the acceleration as a function of time and sketch a graph of the
acceleration vs. time. (b) Determine when the bungee jumper experiences zero acceleration.
(c) Determine the time at which the bungee stops pulling and the person is once again in freefall.
(e) Determine the maximum positive acceleration the bungee jumper experiences.
19. A particle’s velocity is described by the equation v(t) = -6t+4 where the velocity is measured in m/s.
At t=0 s, the particle is at x = 3 m. (a) Determine the acceleration of the particle at 7 s. (b) Determine
the position of the particle at 7 s.
20. Suppose the motion of a rocket can be modeled by the equation a = A + B t0.5. Apply this model to a
rocket with the following initial conditions: when the rocket is launched from rest with initial
acceleration 5.5 m/s2 upward, and it has an acceleration of 13 m/s2 upward 9.0 seconds after launch.
(a) Determine the values of A and B, including units. (b) Find the distance traveled during the first 9.0
seconds. (c) Find the speed at 9.0 seconds.
Motion in 1-Dimension
AP Physics C (mechanics)
Selected Answers
1.
2.
3.
4.
5.
2.65 x 107 m/s
13.6 m/s2 ; 163 m
10.4 s
8.6 s
-0.75 m/s2 ; 176 m
6. t =
; xf =
7. (c) d = 3vt (d) a =
8. 49 m
9. 67 m ; 36 m/s
10. 34.5 m ; 5.3 s
11. 0.53 s
12. 2.52 s ; 0.89 s ; -16.7 m/s
13. 9h
14.
; a=16 m/s2
15. (b) 1 m/s ; 2 m/s2
16. (c) x = -16 m (d) v = -24 m/s
17. (b) 21 m/s
18. (b) t= 0.24 s and t = 2.7 s
(c) t = 0 s and t = 2.93 s
(d) at t = 1.47 s, a = 22.5 m/s2
19. (a) a = -6 m/s2 (b) x=-116m at t=7s
20. (a) A= 5.5 and B= 2.5
(b) at t=9s, x = 385 m
(c) at t = 9 s, v=94.5 m/s