Quick questions on Displacement, velocity and acceleration: N(A)-Level Additional Mathematics

Displacement $s$ is the position of the particle measured from a fixed origin, including direction. It is usually a function of time, $s(t)$. A positive displacement means the particle is on the positive side of the origin; a negative displacement means the negative side. Displacement is not the same as distance travelled: a particle that goes out and comes back has zero displacement but a non-zero distance.

Velocity $v$ is the rate of change of displacement with respect to time, so it measures how fast and in which direction the position is changing. The sign of velocity gives the direction of motion:

Acceleration $a$ is the rate of change of velocity with respect to time. It tells you how the velocity is changing:

A particle has velocity $v = 5\ \text{m s}^{-1}$. State its direction of motion and its speed. [2 marks]

A particle has $v = 3\ \text{m s}^{-1}$ and $a = -1\ \text{m s}^{-2}$. Is it speeding up or slowing down? [1 mark]

Explain why a particle can have zero displacement yet have travelled a positive distance. [2 marks]