Physics Chapter 2 Study Guide

Motion in One-Dimension

 

Frame of Reference

Frame of Reference: a system for specifying the precise location of objects in space and time.

Frame of reference Visual Concept

 

Displacement

Displacement is the change in position of an object.

displacement

 

To calculate displacement you take the final position minus the initial position.

displacement equation

 

Displacement Visual Concept

 

Displacement does not always have to be only in the horizontal direction, it can also be in the vertical direction.

displacement y

 

Example of signs for displacement

displacement signs

 

Velocity

 

Average velocity: the total displacement divided by the time interval during which the displacement occurred.

velocity equation

 

Velocity Visual Concept

 

Velocity versus Speed

Velocity has both a magnitude (How fast it is going.) and a direction.

average speed

 

Graphical Interpretations

 

position graph

 

To find the velocity of the object you must calculate the slope of the position vs time graph.

For example, in the graph above the slope would be found using the points (0, 100) and (4, 1150). This gives

slope

This means the object, a plane in this case, is travelling at 250 m/s.

 

The velocity vs time graph for this example is below.

velocity graph

 

If the position vs time graph is not linear, for example a parabola as in the graph below, then the slope changes constantly.

position graph

 

Finding the slope at different times leads to a linear graph for velocity.

velocity graph

 

Acceleration

Acceleration is the rate at which velocity changes over time; an object accelerates if its speed, direction, or both change.

acceleration

 

Acceleration Visual Concept

 

Example:

Find the acceleration of an amusement park ride that falls from rest to a speed of 28 m/s in 3.0 s.

 

 

 

 

 

 

 

 

 

Acceleration has both a direction and magnitude.

Looking at a velocity vs time.

acceleration

Point A has a positive slope, therefore it is speeding up.

Point B has zero slope, therefore it is moving at constant speed.

Point C has a negative slope, therefore it is slowing down.

 

Graphical Acceleration Visual Concept

 

Sign Conventions for acceleration

acceleration

 

Kinematic Formulas with Constant Acceleration

kinematic equation

 

Example:

A bicyclist accelerates from 5.0 m/s to 16 m/s in 8.0 s. Assuming uniform acceleration, what distance does the bicyclist travel during this time interval?

 

 

 

 

 

 

 

 

 

 

kinematics equation

 

kinematics equation

 

Example:

An aircraft has a landing speed of 83.9 m/s. The landing area of an aircraft carrier is 195 m long. What is the minimum uniform acceleration required for a safe landing.

 

 

 

 

 

 

 

 

 

 

 

Example:

An electron is accelerated uniformly from rest in an accelerator at example over a distance of 95 km. Assuming constant acceleration, what is the final velocity of the electron?

 

 

 

 

 

 

 

 

 

 

Example:

A woman driving at a speed of 23 m/s sees a deer on the road ahead and applies the brakes when she is 210 m from the deer. If the deer does not move and the car stops right before it hits the deer, what is the acceleration provided by the car's brakes?

 

 

 

 

 

 

 

 

 

 

Example:

acceleration graph

Refer to the figure to find the acceleration of the moving object at each of the following times.
A. during the first 5.0 s of travel
B. between 5.0 s and 10.0 s
C. between 10.0 s and 15.0 s
D. between 20.0 s and 25.0 s

 

 

 

 

 

 

 

 

 

 

Example:

displacement

Refer to the figure to find the distance traveled during the following time intervals.
A. t = 0.0 s and t = 5.0 s
B. t = 5.0 s and t = 10.0 s
C. t = 10.0 s and t = 15.0 s
D. t = 0.0 s and t = 25.0 s

 

 

 

 

 

 

 

 

 

Example:

A race car can be slowed with a constant acceleration of example.
A. If the car is going 55 m/s, how many meters will it travel before it stops?

 

 

 

 

 

 

 

B. How many meters will it take to stop a car going twice as fast?

 

 

Free Fall

Free fall is the motion of a body when only the force due to gravity is acting on the body.

Create Table in Class

 

Free Fall Visual Concept

Free Fall Visual Concept 2

Free Fall Visual Concepts 3

 

Example:

A construction worker accidentally drops a brick from a high scaffold.
a. What is the velocity of the brick after 4.0 s?
b. How far does the brick fall during this time?

 

 

 

 

 

 

 

 

 

 

Example:

A student drops a ball from a window 3.5 m above the sidewalk. How fast is it moving when it hits the sidewalk?

 

 

 

 

 

 

 

 

 

 

Example:

A tennis ball is thrown straight up with an initial speed of 22.5 m/s. It is caught at the same distance above the ground.
a. How high does the ball rise?
b. How long does the ball remain in the air?

 

 

 

 

 

 

 

 

 

 

Example:

You throw a ball downward from a window at a speed of 2.0 m/s. How fast will it be moving when it hits the sidewalk 2.5 m below? If the ball is thrown upward instead of downward, how fast will it be moving when it hits the sidewalk?