# acceleration

## velocitytime graphs

The acceleration of an object can be represented by a velocity-time graph like the one in Figure 12.13. A velocity- time graph shows how velocity changes over time. It is similar to a distance-time graph except the y axis represents velocity instead of distance. The graph in Figure 12.13 represents the velocity of a sprinter on a straight track. The runner speeds up for the first 4 seconds of the race, then runs at a constant velocity for the next 3 seconds, and finally slows to a stop during the last 3 seconds of the race. In a velocity-time graph, acceleration is represented by the slope of the graph line. If the line slopes upward, like the line between A and B in Figure 12.13, velocity is increasing, so acceleration is positive. If the line is horizontal, as it is between B and C, velocity is not changing, so acceleration is zero. If the line slopes downward, like the line between C and D, velocity is decreasing, so acceleration is negative. You can review the concept of acceleration as well as other chapter concepts by watching the musical video at this URL:

## calculating acceleration

Calculating acceleration is complicated if both speed and direction are changing. Its easier to calculate acceleration when only speed is changing. To calculate acceleration without a change in direction, you just divide the change in velocity (represented by Dv) by the change in time (represented by Dt). The formula for acceleration in this case is: Acceleration = Dv Dt Consider this example. The cyclist in Figure 12.12 speeds up as he goes downhill on this straight trail. His velocity changes from 1 meter per second at the top of the hill to 6 meters per second at the bottom. If it takes 5 seconds for him to reach the bottom, what is his acceleration, on average, as he flies down the hill? Acceleration = Dv 6 m/s 1 m/s 5 m/s 1 m/s = = = = 1 m/s2 Dt 5s 5s 1m In words, this means that for each second the cyclist travels downhill, his velocity increases by 1 meter per second (on average). The answer to this problem is expressed in the SI unit for acceleration: m/s2 ("meters per second squared"). You Try It! Problem: Tranh slowed his skateboard as he approached the street. He went from 8 m/s to 2 m/s in a period of 3 seconds. What was his acceleration?

## defining acceleration

Acceleration is a measure of the change in velocity of a moving object. It shows how quickly velocity changes. Acceleration may reflect a change in speed, a change in direction, or both. Because acceleration includes both a size (speed) and direction, it is a vector. People commonly think of acceleration as an increase in speed, but a decrease in speed is also acceleration. In this case, acceleration is negative. Negative acceleration may be called deceleration. A change in direction without a change in speed is acceleration as well. You can see several examples of acceleration in Figure 12.11. If you are accelerating, you may be able to feel the change in velocity. This is true whether you change your speed or your direction. Think about what it feels like to ride in a car. As the car speeds up, you feel as though you are being pressed against the seat. The opposite occurs when the car slows down, especially if the change in speed is

## instructional diagrams

As time increases, distance increases as well. Over time, there is a steady speed and then a straight line indicates a stationary moment in time. It then returns to the start.

Figure 1 presents different velocity-time graphs. A velocity-time graph shows how an object's velocity or speed changes over time. The y axis represents velocity (v), while the x axis represents time (t). In the graph for constant velocity, the line remains horizontal, showing that the velocity of the object does not change over time. In the graph for constant acceleration, the line slopes upwards, showing that the velocity of the object increases over time. This increase in velocity is called acceleration. In the graph for constant retardation, the line slopes downwards, which means that velocity decreases over time. This decrease is called retardation. Retardation can also be called negative acceleration or deceleration. A moving object can both accelerate and decelerate. In the graph for irregular motion, the line moves up and down. This means that the velocity of object increases and decreases several times.

This Diagram shows a Velocity-time that is used for determine the acceleration of an object. The vertical axis of a velocity-time graph is the velocity of the object and the horizontal axis is the time taken from the start. When an object is moving with a constant velocity, the line on the graph is horizontal. When an object is moving with a steadily increasing velocity, or a steadily decreasing velocity, the line on the graph is straight, but sloped. The diagram shows some typical lines on a velocity-time graph. The steeper the line, the more rapidly the velocity of the object is changing. The blue line is steeper than the red line because it represents an object that is increasing in velocity much more quickly than the one represented by the red line.

## questions

Acceleration occurs whenever an object

``````a. moves.

b. changes position.

-->  c. changes direction.

d. two of the above
``````

speed plus direction of motion

``````a. acceleration

b. t

c. deceleration

d. speed

e. v

-->  f. velocity

g. m/s2
``````

negative acceleration

``````a. acceleration

b. t

-->  c. deceleration

d. speed

e. v

f. velocity

g. m/s2
``````

Which of the following is an example of acceleration?

``````a. a top spinning at a constant speed

b. a car slowing down through an intersection

c. a train going a steady 80 km/h along a straight track

-->  d. two of the above
``````

What is the acceleration of a bicycle that goes from 3 m/s to 1 m/s in 2 seconds?

``````a. 0.5 m/s2

b. 1.0 m/s2

c. 1.5 m/s2

-->  d. -1.0 m/s2
``````

SI unit for acceleration

``````a. acceleration

b. t

c. deceleration

d. speed

e. v

f. velocity

-->  g. m/s2
``````

symbol for a change in velocity

``````a. acceleration

b. t

c. deceleration

d. speed

-->  e. v

f. velocity

g. m/s2
``````

If the line of a velocity-time graph slopes upward, then acceleration must be

``````a. zero.

-->  b. positive.

c. negative.

d. changing.
``````

measure of a change in velocity

``````-->  a. acceleration

b. t

c. deceleration

d. speed

e. v

f. velocity

g. m/s2
``````

The x-axis of a velocity-time graph represents

``````a. speed.

b. velocity.

c. direction.

-->  d. none of the above
``````

symbol for a change in time

``````a. acceleration

-->  b. t

c. deceleration

d. speed

e. v

f. velocity

g. m/s2
``````

how quickly an object changes position

``````a. acceleration

b. t

c. deceleration

-->  d. speed

e. v

f. velocity

g. m/s2
``````

Acceleration is a vector.

``````-->  a. true

b. false
``````

Acceleration shows how quickly velocity changes.

``````-->  a. true

b. false
``````

A change in direction without a change in speed is not acceleration.

``````a. true

-->  b. false
``````

A velocity-time graph shows how velocity changes over time.

``````-->  a. true

b. false
``````

Acceleration is always greater than or equal to zero.

``````a. true

-->  b. false
``````

Acceleration occurs only when there is a change in speed.

``````a. true

-->  b. false
``````

It is easier to calculate acceleration when both speed and direction are changing.

``````a. true

-->  b. false
``````

The y-axis of a velocity-time graph represents distance traveled.

``````a. true

-->  b. false
``````

If a velocity-time graph slopes downward to the right, then acceleration is negative.

``````-->  a. true

b. false
``````

If velocity is not changing, then acceleration is zero.

``````-->  a. true

b. false
``````

A change in direction with or without a change in speed is velocity.

``````a. true

-->  b. false
``````

If the slope of a velocity-time graph is a straight line, then velocity must be constant.

``````a. true

-->  b. false
``````

Acceleration shows

``````a. how quickly an object travels.

b. the direction in which an object moves.

c. how far an object travels in a given time.

-->  d. how quickly an objects velocity changes.
``````

Which of the following is an example of acceleration?

``````a. a change in direction

b. an increase in speed

c. a decrease in speed

-->  d. all of the above
``````

If you are riding in a car that decelerates suddenly, you will feel your body

``````a. pressed backward.

b. pushed to the side.

-->  c. thrust forward.

d. none of the above
``````

To calculate acceleration without a change in direction, you should use the formula

``````a. acceleration = v + t

b. acceleration = t/v

-->  c. acceleration = v/t

d. acceleration = v  t
``````

When Sara ran a race on a straight track, her speed changed from 3 m/s to 6 m/s over a time period of 3 seconds. What was her acceleration during that time?

``````a. 3 m/s2

-->  b. 1 m/s2

c. 2 m/s2

d. none of the above
``````

What does a velocity-time graph represent?

``````a. how velocity changes over time

b. how distance changes over time

c. acceleration

-->  d. two of the above
``````

If speed decreases, then acceleration is

``````a. zero.

b. positive.

-->  c. negative.

d. between 0 and 1.
``````

## diagram questions

Based on the diagram below, what do you call the state in which the parachutist reaches maximum velocity?

``````a. second terminal velocity

-->  b. first terminal velocity

c. initial acceleration

d. ground reached
``````

What happened if the velocity increases?

``````a. The parachutist will reach the ground slower

b. Nothing happens

-->  c. The parachutist will reach the ground faster

d. First terminal velocity becomes 0
``````

What happens to velocity when the ground is reached?

``````a. It becomes terminal

b. It becomes greater

c. It becomes lesser

-->  d. It becomes zero
``````

What does the blue curved line represent?

``````a. steady speed

-->  b. increasing acceleration

c. deceleration

d. acceleration
``````

Where is the negative acceleration shown on the Velocity Time Graph?

``````a. 20 seconds

b. 50 seconds

c. 90 seconds

-->  d. 40 seconds
``````

What is the velocity at 40 seconds?

``````-->  a. 0 m/s

b. 0.1 m/s

c. 20 m/s

d. 60 m/s
``````

How many labels are in the diagram?

``````a. 3

b. 4

c. 2

-->  d. 6
``````

How much time in seconds is spent accelerating?

``````a. 10

-->  b. 20

c. 5

d. 30
``````

At what time does deceleration happen in the graph?

``````-->  a. At 40 seconds.

b. At 20 seconds in.

c. At 50 seconds.

d. Right from the start.
``````

What does the red line represent in this graphic?

``````a. acceleration

b. deceleration

c. increasing speed

``````

From the diagram, identify the graph that shows constant acceleration.

``````a. E

-->  b. B

c. D

d. C
``````

Which graph is apt for an object travelling at a constant speed?

``````a. D

-->  b. B

c. A

d. C
``````

Out of the following graphs, which one represents linear growth?

``````a. D

b. C

c. A

-->  d. B
``````

Which diagram shows that as time increases, distance remains the same?

``````a. B

b. F

-->  c. A

d. E
``````

How many graphs have curved lines?

``````-->  a. 2

b. 4

c. 5

d. 3
``````

Which graph shows zero acceleration?

``````a. D

b. C

c. B

-->  d. A
``````

Which graph shows a V value in a straight line parallel to t?

``````a. distance changing

b. speed decreasing

-->  c. constant speed

d. speed increasing
``````

In the CONSTANT SPEED graph, if deceleration was observed at the end of the red line, how would the red line change?

``````a. the red line would go upward

-->  b. the red line would would drop downward

c. the red line would continue in a straight line

d. the red line would go down and then go back upward
``````

What is the acceleration when the particle has a velocity profile like the third graph?

``````a. Not able to determine.

b. Constant

c. Equals the velocity.

-->  d. Zero.
``````

How graphs show that speed is changing?

``````a. 0

-->  b. 2

c. 1

d. 3
``````

What happens to the graph when an object is moving with a steadily increasing velocity?

``````a. The line on the graph will be horizontal

b. There will be no line visible

c. The line on the graph will be zigzag

-->  d. The line on the graph will be straight, but sloped.
``````

What increases with when acceleration increases?

``````a. Time

b. Position

-->  c. Velocity

d. Force
``````

Which graph shows a velocity value in a straight line parallel to time?

``````a. negative acceleration

b. positive quaternion

c. positive acceleration

-->  d. positive velocity
``````

Which line corresponds to slowing down in the graph?

``````a. green line

b. blue line

-->  c. orange line

d. red line
``````

What happens when distance and time are increasing?

``````-->  a. We are getting faster

b. We are getting slower

d. We are stationary
``````

What is the diagram showing?

``````a. Speed and Energy

b. Battery and Distance

-->  c. Distance and Time

d. Energy and Power
``````

Identify the figure with zero acceleration.

``````a. Constant acceleration

-->  b. Constant velocity

c. Constant deceleration

d. I don't know
``````

What does a diagram going in the top-right direction indicate?

``````a. Constant speed

b. Constant velocity

c. Constant deceleration

-->  d. Constant acceleration
``````

How many diagonal lines are shown in the diagram?

``````a. 6

-->  b. 3

c. 4

d. 5
``````

In the first graph, what will happen to the velocity bar if time is extended?

``````a. It will begin to fall downwards due to deceleration.

b. It will begin to climb upwards because of acceleration.

-->  c. It will not change direction because velocity is constant.

d. It will alternately climb and fall.
``````

What type of acceleration is done by constant increase of both velocity and time?

``````a. constant deceleration to rest

b. constant deceleration

c. constant velocity

-->  d. constant acceleration
``````

What is the maximum speed in before deceleration?

``````a. 40 m/min

-->  b. 60 m/min

c. 20 m/min

d. 80 m/min
``````

How many times did the velocity change in the graph?

``````-->  a. 3

b. 2

c. 4

d. 1
``````

What is happening from 0 to 10 seconds?

``````a. constant speed

b. reversing

-->  c. accelerating up

d. slowing down
``````

What is the maximum velocity attained?

``````-->  a. 60

b. 40

c. 100

d. 80
``````

What does the slope in a velocity-time graph represent?

``````a. Time

b. Speed

-->  c. Acceleration

d. Distance
``````

What is the velocity at 25 seconds?

``````a. 5

b. 10

-->  c. 0

d. -10
``````

Which type of velocity follows a positive, linear pattern of growth?

``````-->  a. constant velocity

b. decelerating

c. zero velocity

d. accelerating
``````

Which velocity time graph is applicable when you brake to stop your car?

``````a. Zero velocity

b. Constant velocity

c. Accelerating

-->  d. Decelerating
``````

Which graph shows an increase in velocity?

``````a. constant velocity

b. constant deceleration

c. all of the above

-->  d. Constant acceleration
``````

At constant velocity, which is the acceleration?

``````-->  a. 0

b. The same as the second graph.

c. The same as the first graph.

d. Equals to V = 0.
``````

Which graph shows something slowing down?

``````a. None

-->  b. Deceleration

c. Constant velocity

d. Acceleration
``````

DO either of these graphs show zero accelerations?

``````a. Graph 2 shows zero acceleration

-->  b. No it does not

c. Graph 1 shows zero acceleration

d. Both show zero acceleration
``````

In acceleration, what happens if the Time increases?

``````-->  a. Acceleration decreases

b. acceleration increases

c. nothing happens

d. time decreases
``````

Does the blue line increase or decrease on deceleration?

``````-->  a. decrease

b. increase

c. stay the same

d. curves
``````