Question

A motor scooter travels east at a speed of $13m/s$. The driver then reverses direction and heads west at $17m/s$. What was the change in velocity of the scooter? (in$m/s$)
$(A)4$
$(B)30$
$(C)32$
$(D)\;21$

Answer 1

The question relies on the relative velocity. Relative velocity is the velocity which is taken out with relevance to another body; usually the relative velocity is taken out between two moving bodies; the body is within the same or different direction. The speed of a body with relevance to the speed of another body is termed as the relative velocity of the primary body with relevance to the second.
Formula used:
$\Delta v = v - u$, Where $u$-initial velocity and $v$-final velocity and $\Delta v$- change in velocity.

Complete step-by-step solution:
Complete step by step answer:
Given data: Initial velocity $u = - 13m/s$, consider the direction of east to be a negative direction
Final velocity $v = 17m/s$, Consider the direction of the west to be a positive direction.
Thus the change in velocity $\Delta v = v - u = 17 - \left( { - 13} \right) = 30m/s$
Hence, option B is correct. The change in velocity of the scooter is $30m/s$.

Additional information:
Velocity could be a vector measurement of the rate of motion of an object and also the direction during which it’s moving. Hence, to work out the velocity as per this definition, we must always be accustomed to both the magnitude and direction. For example, if an object travels towards the west at 5 meters per second (m/s), then its velocity is $5m/s$ to the west.

Note: Students must be careful about the direction of the velocity vector when calculating the relative velocity. Also always remember that for relative velocity there should be only one coordinate system. Hence, the negative sign indicates that the direction of the velocity with relevance to the observer on the ground is from west to east. Also, the positive sign indicates that the direction of the velocity with relevance to the observer on the ground is from east to west.