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

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 - initial velocity

\Delta v = v - u

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

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

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

This is when:

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

If an object is slowing down, it is decelerating (and 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.

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

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

a = 28 \div 8

\alpha = 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

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

\alpha = 10 \div 25

\alpha = 0.4~m/s^2