Question

A scooter going to the east at 10 m/s turns right through an angle of ${90}^{\circ }$. If the speed of the scooter remains unchanged in taking this turn, the change in the velocity of the scooter is:

• A. 20 m/s in south-west direction
• B. zero
• C. 10.0 m/s in south direction
• D. 14.14 m/s in south-western direction

Answer 1

The correct option is D 14.14 m/s in south-western direction

If we use vector notation to write our velocities,

initial velocity is, $v_i=10\hat{i}m/s$

final velocity is, $v_f=-10\hat{j}m/s$

So the change in velocity is, $\Delta v=v_f-v_i=10(-\hat{i}-\hat{j})m/s$

magnitude of change in velocity is, $|\Delta v|=\sqrt{{10}^2+{10}^2}=14.14m/s$

Direction is south-western.