Acceleration

Acceleration is the rate of change of velocity.

It’s basically how quickly something speeds up.

Because it’s the rate of change of velocity, it’s a vector quantity.

\text{acceleration}=\text{velocity}\div\text{time}

v=at

a=\frac vt

Calculations

The velocity of a car increases from 10ms^{-1} to 30ms^{-1} in 4s. Calculate its acceleration.

• In this case we need to use the change in velocity, \Delta v.
• \Delta v=30-10=20
• a=\frac{\Delta v}t
• a=\frac{20}4=5
• Answer: 5ms^{-1}

A car accelerates at 2ms^{-2} for 5s. Calculate the change in velocity.

• a=\frac{\Delta v}t
• \Delta v=at
• \Delta v=2\times5=10
• Answer: 10ms^{-1}

A bike accelerates at 0.5ms^{-2} for 10s. Calculate the change in velocity.

• a=\frac{\Delta v}t
• \Delta v=at
• \Delta v=0.5\times10=5
• Answer: 5ms^{-1}

A car accelerates at 3ms^{-2} until reaching a velocity of 20ms^{-1}. Calculate the time taken to reach this velocity.

• a=\frac vt
• t=\frac v a
• t=\frac{20}3\approx6.67
• Answer: 6.67s

A van accelerates at 4ms^{-2} for 8s. Calculate the change in velocity.

• a=\frac{\Delta v}t
• \Delta v=at
• \Delta v=4\times8=32
• Answer: 32ms^{-1}

A truck accelerates at 5ms^{-2} for 6s. Calculate the change in velocity.

• a=\frac{\Delta v}t
• \Delta v=at
• \Delta v=5\times6=30
• Answer: 30ms^{-1}

A car accelerates at 1ms^{-2} until reaching a velocity of 15ms^{-1}. Calculate the time taken to reach this velocity.

• a=\frac vt
• t=\frac v a
• t=\frac{15}1=15
• Answer: 15s

A bike accelerates at 0.2ms^{-2} for 12s. Calculate the change in velocity.

• a=\frac{\Delta v}t
• \Delta v=at
• \Delta v=0.2\times12=2.4
• Answer: 2.4ms^{-1}

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