Question

Give one example of motion in which a body has constant speed but not constant velocity?

Answer 1

Example : Uniform circular motion, the acceleration resulting from the change in direction of the body which travels at constant speed.

Explanation:

Uniform motion (CCW round the unit circle to keep simple as poss):

• `x = cos omega t, qquad y = sin omega t, qquad bbr = langle x, y rangle`

`dot x = - omega sin omega t, qquad dot y = omega cos omega t`

Velocity `bbv = omega langle - sin omega t, cos omega t rangle ne " const"`

Speed `dot s = sqrt(dot x^2 + dot y^2) = omega = " const"`

Acceleration :

• `ddot x = - omega^2 cos omega t, qquad ddot y = -omega^2 sin omega t`

• `bba = - omega^2 bb r`, ie accelerates constantly toward the centre of the motion

• `abs bb a = omega^2`