Distance/Speed/Acceleration Revision Notes for Leaving Cert Mathematics

Distance/Speed/Acceleration

Calculus has a very important application in relation to distance, speed and acceleration.

Distance (or displacement) describes the position of an object relative to a reference point at a given time $t$ . It is the primary quantity that changes over time due to motion.
Velocity is the rate of change of distance with respect to time. It measures how fast an object's position is changing.

Acceleration is the rate of change of velocity with respect to time. It measures how fast an object's velocity is changing.

Example

infoNote

The distance $s$ (in metres) of a car from point $P$ after $t$ seconds is given by

s=3t^2+2

The velocity of the car is simply the first derivative of displacement (distance)

s'=v=6t

The acceleration of the car is the first derivative of velocity (or the second derivative of displacement).

s''=v'=6