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.

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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.

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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

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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

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