EXAMPLE 1: Consider the velocity vs. time graph below. The motion of five different people (A, B, C, D, and E) are shown on the graph. Study the graph and answer the following questions. Some questions may have more than or less than one answer.

Question:

1. Which person(s) changes direction during the time of motion?

2. Which person(s) is/are not moving?

3. Which person has the greatest average speed?

4. Which person(s) has/have a constant, positive acceleration value?

5. Which person has the greatest magnitude of acceleration?

1. C

2. none

3. E

4. D reason: lets say initial vel = -100, and final velocity = -50 -> a = vf – vi/t = -50 – (-100) = +50/t

5. C (largest change in velocity)

EXAMPLE

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dnorth = dsouth at catch up points

Since the train leaving the South is designated as having a negative velocity, it starts at 150 km point and the train leaving the North starts at 0 (as the slope of the velocity is positive) dsouth = vsoutht + do dnorth = vnortht vsoutht + do = vnortht

-65t + 150 = 55t t = 1.25 = 1.3 hours

Substitute t into one of the equations to find the distance when they pass:

dsouth = vsoutht + do = -65(1.25) + 150 = 68.75 = 69 km from the North Why is it from the North? (look to graph for answer, what does d represent)

EXAMPLE 5: A ball is thrown vertically upward from a window that is 3.6 m above the ground. The ball's initial speed is 2.8 m/s and the acceleration due to gravity is 9.8 m/s2.

(a) What is the ball's speed when it hits the ground?

(b) How long after the first ball is thrown should a second ball be simply dropped from the same window so that both balls hit the ground at the same time?

NOTE: Let down be the "negative" direction and up be the "positive" direction.

a. vf = (vi2 + 2ad)1/2

vf = [2.82 + 2(-9.8)(3.6)]1/2

vf = 8.9 m/s

b. The ball's speed is 8.9

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An object with a positive acceleration will be represented on a position-time graph by a line which curves upwards.

i. An object with a negative acceleration will be represented on a position-time graph by a line which curves downwards.

6. Which of the following statements about velocity-time graphs are TRUE? List all that apply.

a. The slope on a velocity-time graph is representative of the acceleration of the object.

b. The area on a velocity -time graph is representative of the change in position of the object.

c. An accelerated object's motion will be represented by a curved line on a velocity-time graph.

d. Objects with positive acceleration will be represented by upwardly-curved lines on a velocity-time graph.

e. If an object is at rest, then the velocity-time graph will be a line with zero slope.

f. A line with zero slope on a velocity-time graph will be representative of an object which is at rest.

g. A line with a negative slope on a velocity-time graph is representative of an object with negative velocity.

h. If an object changes its direction, then the line on the velocity-time graph will have a changing slope.

i. An object which is slowing down is represented by a line on a velocity-time graph which is moving in the downward