Velocity 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

Acceleration

When people run, fall, cycle or travel in a car or a plane their speed will change. They may speed up - acceleration, or slow down - deceleration. 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\ \text{-}\ initial\ velocity

\Delta v = v\ \text{-}\ u

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

acceleration = \frac{change\: in\: velocity}{time\: taken}

a = \frac{\Delta v}{t}

This is when:

  • acceleration (a) is measured in metres per second squared (m/s²)
  • change in velocity (∆v) is measured in metres per second (m/s)
  • time taken (t) for the change in velocity is measured in seconds (s)

If an object is slowing down, it is decelerating (and its acceleration has a negative value). Some typical values for acceleration in metres per second (m/s²) include:

Method of travel Typical acceleration in m/s²
Running from a standing start6
Family car overtaking another car on a motorway4
Skydiver falling under the action of gravity10
Rollercoaster going into a loop 30 - 60
Race car leaving the starting grid in a race14

Example

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

final velocity, (v) = 28 m/s

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

change in velocity, (∆v) = (28 – 0) = 28 m/s

a = \frac{\Delta v}{t}

a=28\div8

\underline{a=3.5\:m/s^{2}}

Question

A car takes 25 s to accelerate from 20 m/s to 30 m/s. Calculate the acceleration of the car.

final velocity, (v) = 30 m/s

initial velocity, (u) = 20 m/s

change in velocity, (∆v) = (30 – 20) = 10 m/s

a = \frac{\Delta v}{t}

a=10\div25

\underline{a=0.4\: m/s^{2}}

Question

A bicycle is moving at 10 m/s when the rider applies the brakes and stops in 5 seconds. What is the acceleration?

final velocity, (v) = 0 m/s

initial velocity, (u) = 10 m/s

change in velocity, (∆v) = (0 − 10) = -10 m/s

a = \frac{\Delta v}{t}

a= -10\div5

\underline{a=-2\: m/s^{2}}

The answer is a negative acceleration so the bicycle is decelerating.