### GCSE Physics

Energy
Forces
Forces and Motion
Waves in Matter
Electricity
Magnetism and Electromagnetism
Particle Model of Matter
Atomic Structure
Space Physics

# Velocity-Time Graphs

Velocity-time graphs show us how an object’s velocity changes over time. You can see an example of a velocity-time graph below.

• In the graph, velocity (measured in m/s) is on the y-axis and time (in seconds) is on the x-axis.

Velocity-time graphs also show if an object has constant acceleration or deceleration, as well as its magnitude.

We can calculate the acceleration of an object by using the equation:

• a = Acceleration in metres per second squared (m/s2)
• Δv = Change in velocity in metres per second (m/s)
• t = time taken in seconds (s)

## Features of Velocity-Time Graphs

When looking at velocity-time graphs, we can observe important features:

• Straight lines indicate a constant acceleration – A constant gradient
• Horizontal lines indicate a constant velocity – No acceleration, so the gradient is 0
• A steepening curve indicates an increasing acceleration – An increasing gradient
• A downward-sloping line indicates deceleration – The object is slowing down, so there is a negative gradient

## Distance Travelled

To calculate the distance travelled, we can calculate the area under the curve. With the example below, we can separate the area into two triangles and a rectangle.

The equation to calculate the area of a rectangle is:

The area of the rectangle = (50 − 20) × (60 − 0) = 30 × 60

= 1800 m

The equation to calculate the area of a triangle is:

Area of triangle 1 = 0.5 × (20 − 0) × (60 − 0) = 0.5 × 20 × 60

= 600 m

Area of triangle 2 = 0.5 × (80 − 50) × (60 − 0) = 0.5 × 30 × 60

= 900 m

Therefore, the total distance travelled is 3,300 m (1,800 m + 600 m + 900 m).

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