AP Physics 1 Kinematics
AP Physics 1
Kinematics
Kinematics
Study of Motion
Distance
Total distance traveled from start to finish.
Displacement Straight line distance between the start point and ending point of the problem.
Speed
A scalar quantity (no direction specified) that shows the rate that distance is covered.
Instantaneous
The speed at an instant in time. Right now. Your speedometer reading when you glance at it.
Average
The total distance divided by the total time for the entire trip.
Constant
If the same speed is maintained over the entire trip
Velocity
A vector quantity consisting of magnitude and direction. Displacement x divided by time interval.
Acceleration Change in velocity over a time interval. Acceleration happens when you speed up, slow down or change
direction.
Kinematic Equations
You can only use the constant velocity equation when there is no acceleration. If acceleration is present (question
contains terms such as: starts from rest, final velocity of, accelerates, comes to rest, etc.), then you must use the
Kinematic equations in the highlighted boarder boxes below.
Constant Speed or Constant Velocity
v?
Average Velocity
x ? xo
v?
t
x
t
Acceleration
a?
v ? vo
t
v ? vo ? at
Velocity
Rearrange the acceleration equation from above. Useful for
determining v, when a and t are given.
1
x ? xo ? vot ? at 2
2
Position
Key equation to determine position when a is involved. Used
extensively in free-falling problems where a = g
v 2 ? vo ? 2a ? x ? xo ?
2
When no time is given
When v, a, and/or x are known, but no information is given about t,
then this can be used to solve for the unknown variable.
xo initial position, x final position, vo initial velocity, v final velocity, a acceleration, t time
Acceleration and Velocity
If velocity and acceleration have the same sign: object is speeding up.
If velocity and acceleration have opposite signs: object is slowing down.
Falling Objects
Acceleration:
2
If object fired downward, g = + 9.8 m/s . If object fired upward g = - 9.8 m/s
2
Projectile Motion
Motion in two dimensions happens simultaneously.
? In the x direction the velocity is constant, with no acceleration occurring.
? In the y direction the acceleration due to gravity slows upward motion and increases downward motion.
? At the highest point in the trajectory of a projectile only the vertical velocity component vy of the velocity is
zero, but the vertical component of the acceleration is g and is directed downward.
1
KINEMATICS GRAPHS
I. Uniform Motion: Constant velocity
Position-Time Graph
Object is at rest.
Object is moving to the left (negative direction).
Object is at rest.
Velocity-Time Graph
Object is at rest.
Object is moving in the negative direction at constant
speed. Look at the slope of x-t graph.
Object is at rest.
Acceleration-Time Graph
Acceleration is zero in all parts of motion since object
is either at rest or moving at constant speed.
I. Uniform Accelerated Motion
This set of graphs could represent an object
thrown up (free fall)
Position-Time Graph
Object first moves in the positive direction and
comes back to the initial position.
Velocity-Time Graph
Object starts with a positive velocity, slows down
while moving in the negative direction.
Object changes direction.
Object continues moving in the negative direction.
Acceleration-Time Graph
Acceleration is constant and negative for all parts of
motion.
2
GRAPHICAL ANALYSIS
PROJECTILE MOTION
Projectile fired horizontally and
free-falling object
A ball rolled off a horizontal table will take the
same amount of time to hit the ground as another
dropped from the same height.
t?
Projectile fired at an angle and object
thrown up in free-fall
Compare velocities at equal positions on the way up and down.
tup = tdown for objects returning to ground level
2y
g
t?
Horizontal component of velocity graphs
Vertical component of velocity graphs
3
2v0 sin ?
g
EXERCISES:
1. A person initially at point P in the illustration stays there a moment and then moves along the axis to Q and stays there
a moment. She then runs quickly to R, stays there a moment, and then strolls slowly back to Q .Which of the position vs.
time graphs below correctly represents this motion?
2. A person standing at the edge of a cliff throws one ball straight up and another ball straight down at the same initial
speed. Neglecting air resistance, the ball to hit the ground below the cliff with the greater speed is the one initially thrown
(A) upward.
(B) downward.
(C) neither¡ªthey both hit at the same speed.
3. A train car moves along a long straight track. The graph shows the position as a function of time for this train. The
graph shows that the train:
(A) speeds up all the time.
(B)slows down all the time.
(C) speeds up part of the time and slows down part of the time.
(D) moves at a constant velocity.
4. You are throwing a ball straight up in the air. At the highest point, the ball¡¯s
(A) velocity and acceleration are zero.
(B) velocity is nonzero but its acceleration is zero.
(C) acceleration is nonzero, but its velocity is zero.
(D) velocity and acceleration are both nonzero.
5. The graph shows position as a function of time for two trains running on parallel tracks. Which is true:
(A) At time tB,both trains have the same velocity.
(B) Both trains speed up all the time.
(C) Both trains have the same velocity at some time before tB.
(D) Somewhere on the graph, both trains have the same acceleration.
6. A cart on a roller coaster rolls down the track shown below. As the cart rolls beyond the point shown, what happens to
its speed and acceleration in the direction of motion? Ignore any effects of friction.
(A) Both decrease.
(B) The speed decreases, but the acceleration increases.
(C) Both remain constant.
(D) The speed increases, but acceleration decreases.
(D) Both increase
4
7. Consider the situation depicted here. A gun is aimed directly at a dangerous criminal hanging from the gutter of a
building. The target is well within the gun¡¯s range, but the instant the gun is fired and the bullet moves with a speed vo, the
criminal lets go and drops to the ground. What happens? The bullet
(A) hits the criminal regardless of the valueof vo.
(B) hits the criminal only if vo is large enough.
(C) misses the criminal.
8. A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which
ship gets hit first?
(A) Ship A
(B) both at the same time
(C) Ship B
(D) need more information
9. A car starts from some point P, drives 10 km to a point Q, and then returns to P. The car completes the trip in 10 min.
Select the correct values for the car¡¯s average velocity and average speed.
average velocity (m/s)
(A)
0
(B)
0
(C)
120 km/h
(D)
120 km/h
average speed (m/s)
0
120 km/h
0
120 km/h
10. Two metal balls are the same size but one weighs twice as much as the other. The balls are dropped from the roof
of a single story building at the same instant of time. The time it takes the balls to reach the ground below will be:
(A) about half as long for the heavier ball as for the lighter one
(B) about half as long for the lighter ball as for the heavier one
(C) about the same for both balls
(D) considerably less for the heavier ball, but not necessarily half as long
11. The two metal balls of the previous problem roll off a horizontal table with the same speed. In this situation:
(A) both balls hit the floor at approximately the same horizontal distance from the base of the table
(B) the heavier ball hits the floor at about half the horizontal distance from the base of the table than does the lighter ball
(C) the lighter ball hits the floor at about half the horizontal distance from the base of the table than does the heavier ball
(D) the heavier ball hits the floor considerably closer to the base of the table than the lighter ball, but not necessarily at
half the horizontal distance
12. An arrow is aimed horizontally, directly at the center of a target 20 m away. The arrow hits 0.050 m below the center
of the target. Neglecting air resistance, what was the initial speed of the arrow?
(A) 20 m/s
(B) 40 m/s
(C) 100 m/s
(D) 200 m/s
13. The graph shows the velocity versus time for an object moving in a
straight line. At what time after t = 0 does the object again pass through its
initial position?
(A) 1 s
(B) Between 1 and 2 s
(C) 2 s
(D) Between 2 and 3 s
5
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