Distance-time and velocity-time graphs

What does a distance–time graph show?

• It shows how an object's distance changes over time.

• Time is on the x-axis.

• Distance is on the y-axis.

What does the gradient of a distance–time graph represent?

• The gradient represents the object's speed.

Equation:

Speed = change in distance ÷ change in time. What does a steep line mean on a distance–time graph?

What does a steep line mean on a distance–time graph?

• A steeper gradient means a greater speed.

• A less steep gradient means a lower speed.

What does a horizontal line mean on a distance–time graph

• The distance is not changing.

• The object is stationary.

• Speed = 0 m/s.

What does a straight diagonal line mean?

• The object is travelling at a constant speed.

• The gradient stays the same.

What does a curved line mean?

• The object's speed is changing.

• A curve getting steeper → speeding up.

• A curve becoming less steep → slowing down.

What does a velocity–time graph show?

• It shows how an object's velocity changes over time.

• Time is on the x-axis.

• Velocity is on the y-axis.

What does the gradient of a velocity–time graph represent?

• The gradient represents acceleration.

Equation:

Acceleration = change in velocity ÷ change in time

How do you calculate acceleration from a velocity–time graph?

Acceleration = (final velocity − initial velocity) ÷ time

Example:

Velocity changes from 5 m/s to 15 m/s in 5 s.

a = (15 − 5) ÷ 5 = 2 m/s²

What does a horizontal line mean on a velocity–time graph?

• Velocity is constant.

• Acceleration = 0 m/s².

The object is still moving if the velocity is above zero!

What does a positive gradient mean?

• Velocity is increasing.

• The object is accelerating.

What does a negative gradient mean?

• Velocity is decreasing.

• The object is decelerating

How do you calculate distance from a velocity–time graph?

• Calculate the area under the graph.

Distance = area under a velocity–time graph

How do you calculate distance when the graph is a rectangle?

Distance = base × height

Example:

Velocity = 10 m/s
Time = 5 s

Distance = 5 × 10 = 50 m

How do you calculate distance when the graph is a triangle?

Distance = ½ × base × height

Example:

Velocity = 10 m/s
Time = 5 s

Distance = ½ × 5 × 10 = 25 m

What if the area under the graph is a rectangle + triangle?

1. Split the shape into simpler shapes.

2. Calculate the area of each.

3. Add the areas together.

Total area = distance travelled