1

This is a velocity/time graph. What does it have in common to a distance/time graph?

2

So both V-T graphs and D-T graphs have time as their independent variable.

They differ in their dependent variables.

3

Let's try reading this graph.

What was this object's velocity after 10 seconds?

4

So at time = 10 seconds, the object was travelling at $15\:m/s$ .

This information is given by the point $(10,15)$ .

5

What was this object's velocity after 20 seconds?

6

True or false? This object was moving faster after 20 seconds than after 10 seconds.

7

After 10 seconds the object was moving with a velocity of $15\:m/s$ , and after 20 seconds it was moving with a velocity of $30\:m/s$ . That means that this object was...

8

So this is a velocity/time graph that shows an accelerating object.

The further out on the x-axis you go, the higher the velocity (m/s) gets.

9

What is the acceleration of this object?

Horizontal Lines

1

How would you describe the motion of this particular object?

2

What is the slope, and thus the acceleration, of this object?

3

So this is a velocity/time graph that shows an object that is moving at constant speed - it has acceleration of $0m/s^2$

No matter when the object's velocity was measured, it was unchanged. It stayed at $40\:m/s$ .

Positive Gradients

1

What is the change in velocity here from 10 seconds to 20 seconds?

2

So at 10 seconds, the velocity is $35\space m/s$ , and at 20 seconds the velocity is $50 \space m/s$ . What is the acceleration in $m/s^2$ over the course of those 10 seconds?

3

Between 10 and 20 seconds, the acceleration of the object is $1.5 \space m/s^2$ . Is that the same between 30 seconds and 40 seconds? Answer yes or no.

4

True or false? This object is moving at constant speed.

5

True or false? This object is speeding up at a constant rate.

6

So, a velocity/time graph with a positive gradient shows an object with a constant (unchanging) acceleration.

We call this uniform acceleration.

Negative Gradients

1

How was the velocity of this object changing over time?

2

So this object was...

3

So this is a velocity/time graph that shows an object that is slowing down or decelerating.

The further out on the x-axis you go, the lower the velocity (m/s) gets.

4

What kind of acceleration does this object have?

5

Calculate the acceleration of this object.

6

So a negative gradient shows negative acceleration. Is this uniform acceleration?

7

So, a velocity/time graph with a constant negative acceleration...

shows the motion of an object with uniform deceleration.

Curved Lines

1

Is the gradient the same at all points on this graph?

2

Was this object speeding up at a constant rate?

3

This curved line shows that the object was speeding up faster and faster

The further out the x-axis you go, the steeper the graph gets, so the larger its acceleration gets.

4

The green line shows an object that is...

5

The green line shows an object which is still speeding up, but at a lower and lower rate

If a curve flattens out in a velocity/time graph, that just means that the object is going towards constant speed. It does not mean the object stops moving!

6

Are these examples of uniform acceleration?

7

So curved lines on a velocity/time graph show...

non-uniform acceleration.

Summary!

1

A velocity/time graph has velocity on the y-axis and time on the x-axis.

The gradient in a velocity/time graph is the same as acceleration $a=\frac{\Delta v}{\Delta t}$ , with units $m/s^2$

2

A horizontal line means the object is moving at a constant speed

This is because it has no gradient, and thus no acceleration.

3

A constant positive gradient means...

the object has a positive uniform acceleration.

4

A constant negative gradient means...

the object has a uniform deceleration.

5

A line that curves upwards means the object is speeding up faster and faster.

Its acceleration is increasing, so it is non-uniform.

6

A line that flattens out means the object is still speeding up, but doing so at a slower and slower rate

Its acceleration is decreasing, so it is non-uniform.

Velocity/Time Graphs

Velocity/Time Graphs