Velocity calculations

This equation applies to objects with a uniform (constant) acceleration:

(final velocity)2 - (initial velocity)2 = 2 × acceleration × distance

This is when:

  • final velocity is measured in metres per second (m/s)
  • initial velocity is measured in metres per second (m/s)
  • acceleration is measured in metres per second squared (m/s²)
  • displacement is measured in metres (m)

Example

A car has an initial velocity of 4 m/s and accelerates at a rate of 2 m/s2 to a final velocity of 18 m/s. What distance is travelled by the car?

Rearrange the equation:

distance = \frac{(final~velocity)^2 - (initial~velocity)^2}{2 \times acceleration}

Then use the values given in the question:

distance = \frac{18^2 - 4^2}{2\times2}

distance = 77 m

Calculating kinetic energy

Energy can be transferred between stores during motion. In the example above, while the car is in motion, the store that changes is the kinetic store. To calculate kinetic energy, use the equation:

kinetic energy = 0.5 × mass × speed 2

This is when:

  • speed is measured in metres per second (m/s)
  • mass is measured in kilograms (kg)
  • kinetic energy is measured in joules (J)

Calculate the initial kinetic store of the car in the previous example, if its mass is 1500 kg. Remember that:

kinetic~energy = \frac{1}{2} \times m \times v^2

kinetic~energy = \frac{1}{2} \times 1,500 \times 4^2

So the value of the kinetic store is 12,000 J or 12 kJ.