Motion - OCR GatewayVelocity and acceleration

The velocity of an object is its speed in a particular direction. Velocity is a vector quantity because it has both a magnitude and an associated direction. To calculate velocity, displacement is used in calculations, rather than distance.

Unlike distance, which is a scalar quantity, displacement is a vector quantity. It includes:

• the distance travelled, measured in a straight line from start to finish
• the direction of the straight line

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Acceleration

Acceleration is the rate of change of velocity. It is the amount that velocity changes per unit time.

The change in velocity can be calculated using the equation:

change in velocity = final velocity - intial velocity

This is when:

• change in velocity is measured in metres per second (m/s)
• final velocity is measured in (m/s)
• initial velocity is measured in seconds (m/s)

The average acceleration of an object can be calculated using the equation:

This is when:

• acceleration is measured in metres per second squared (m/s²)
• change in velocity is measured in metres per second (m/s)
• time taken is measured in seconds (s)

If an object is slowing down, it is decelerating - in this case, its acceleration has a negative value.

Example

A car takes 8.0 s to accelerate from rest to 28 m/s. Calculate the average acceleration of the car.

First calculate change in velocity:

final velocity = 28 m/s

initial velocity = 0 m/s (because it was at rest – not moving)

change in velocity = (28 - 0) = 28 m/s

Then use the values to calculate average acceleration:

acceleration = 28 ÷ 8

acceleration = 3.5 m/s²