AP Physics Chapter 2 Study Guide

Motion in One Dimension

Describing Motion

Sign Conventions for Position

sign conventions

 

Sign Conventions for Velocity

sign conventions

 

Position - versus - time graphs

postion vs. time graph

 

Example 1

What does the graph tell us about the motion?

position graph

 

 

 

 

 

Example 2

A kingfisher is a bird that catches fish by plunging into water from a height of several meters. If a kingfisher dives from a height of 7.0 m with an average speed of 4.00 m/s, how long does it take for it to reach the water?

 

 

 

 

 

 

 

 

Example 3

An athlete sprints 50.0 m in 8.00 s, stops, and then walks slowly back to the starting line in 40.0 s. If the "sprint direction" is taken to be positive, what is
(a) the average sprint velocity

 

 

 

(b) the average walking velocity

 

 

 

(c) the average velocity for the complete round trip?

 

 

 

 

Equations of Uniform Motion

Find the slope of a position-versus-time graph:

 

 

 

 

 

 

 

 

From Velocity to Position

Example 4

What does the graph tell us?

velocity graph

 

 

 

 

 

Example 5

How far does the runner whose velocity-versus-time graph is shown travel in 16 s? The initial velocity is 8.0 m/s.

velocity graph

 

 

 

 

 

Motion with Changing Velocity

Instantaneous Velocity

Changing Velocity Graphs

Changing Velocity Graphs

 

three graphs

 

Acceleration

acceleration

 

velocity

 

sign of acceleration

 

Example 6

The figure is a velocity-time graph for a test car on a straight track. The test car initially moved backward in the negative x-direction at 20 m/s. It slowed, came to a stop, and then moved off in the positive x-direction at t = 2.0 s.
velocity graph
(a) What was its average acceleration during each of the time intervals 0 to 0.5 s, 1.5 s to 2.0 s, and 2.0 s to 2.5 s?

 

 

 

 

 

(b) What was its instantaneous acceleration at t = 2.25 s?

 

 

 

 

Constant Acceleration Equations

equation

equation

equation

 

Constant Velocity

 

constant acceleration

 

 

Example 7

At the 18th green of the U.S. Open you need to make a 20.5 ft putt to win the tournament. When you hit the ball, giving it an initial speed of 1.57 m/s, it stops 6.00 ft short of the hole.
(a) Assume the acceleration caused by the grass is constant, what should the initial speed have been to just make the putt?

 

 

 

 

 

 

 

(b) What initial speed do you need to make the remaining 6.00 ft putt?

 

 

 

 

 

 

 

 

 

Free-Fall

Example 8

A person steps off the end of a 3.00 m high diving board and drops to the water below. (a) How long does it take for the person to reach the water?

 

 

 

 

 

 

 

(b) What is the person's speed on entering the water?

 

 

 

 

 

 

 

 

 

 

 

 

Example 9

You drop a rock from a bridge to the river below. When the rock has fallen 4 m, you drop a second rock. As the rocks continue their free fall, does their separation (a) increase, (b) decrease, or (c) stay the same?

bridge

 

 

 

 

 

Example 10

A volcano shoots out blobs of molten lava, called lava bombs, from ground level. A geologist observing the eruption uses a stopwatch to time the flight of a particular lava bomb that is projected straight upward. If the time for it to rise and fall back to the ground is 4.75 s, and its acceleration is 9.81 m/s^2 downward, what is its initial speed?

volcano

 

 

 

 

 

 

 

 

Example 11

A hot air balloon is rising straight upward with a constant speed of 6.5 m/s. When the basket of the balloon is 20.0 m above the ground a bag of sand tied to the basket comes loose.

balloon
(a) How long is the bag of sand in the air before it hits the ground?

 

 

 

 

 

 

(b) What is the greatest height of the bag of sand during its fall to the ground?

 

 

 

 

 

 

 

 

Example 12

On a hot summer day in the state of Washington while riding my bike, I saw several swimmers jump from a railroad bridge into the Snohomish River below. The swimmers stepped off the bridge, and I estimated that they hit the water 1.5 s. later.
(a) How high was the bridge?

 

 

 

 

(b) How fast were the swimmers moving when they hit the water?

 

 

 

 

 

(c) What would the swimmer's drop time be if the bridge were twice as high?

 

 

 

 

 

 

Example 13

Astronauts on a distant planet throw a rock straight upward and record its motion with a video camera. After digitizing their video, they are able to produce the graph of height, y, versus time, t, shown in the figure.
Graph

(a) What is the acceleration of gravity on this planet?

 

 

 

 

 

 

 

(b) What was the initial speed of the rock?

 

 

 

 

 

 

 

Practice Test Problem

This question concerns the motion of a car on a straight track; the car's velocity as a function of time is plotted below.

final problem

(a) Describe what happened to the car at time t = 1 s.

 

 

 

 

(b) How does the car's average velocity between time t = 0 and t = 1 s compare to its average velocity between times t = 1 s and t = 5 s?

 

 

 

 

 

(c) What is the displacement of the car from time t = 0 to time t = 7 s?

 

 

 

 

(d) Plot the car's acceleration during this interval as a function of time.

 

 

 

 

(e) Make a sketch of the object's position during this interval as a function of time. Assume that the car begins at x = 0.