# Velocity-time graphs

You should be able to explain velocity-time graphs for objects moving with a constant velocity or constant acceleration.

The velocity of an object is its speed in a particular direction. This means that two cars will have different velocities if they are travelling at:

• The same speed but in different directions
• The different speeds in the same direction
• The different speeds in different directions

# Acceleration

You should be able to calculate the acceleration of an object from its change in velocity and the time taken.

## The equation

When an object moves in a straight line with a constant acceleration, you can calculate its acceleration if you know how much its velocity changes and how long this takes. This equation shows the relationship between acceleration, change in velocity and time taken:

a = (v – u) ÷ t

• a is the acceleration of the object in metres per second squared, m/s2
• v is the final velocity in metres per second, m/s
• u is the initial (starting) velocity in metres per second, m/s
• t is the time taken in seconds, s
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## MOTION

Acceleration

Acceleration is the rate at which an object changes its speed. It's calulated using the equation: acceleration = change in speed / time taken.

Speed-time graphs illustrate how the speed of an object changes over time. The steeper the gradient of the line, the greater the acceleration.

In everyday language we use 'accelerate' to mean speeding up and 'decelerate' to mean slowing down. In scientific terms 'acceleration' is the rate at which something changes its speed - faster or slower.

Acceleration depends on two things:

• How much the speed changes
• How much time the change in speed takes
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## Calculating acceleration

acceleration = change in speed / time taken change in speed = acceleration x time taken

time taken = change in speed / acceleration

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