Question

A car moving with a speed of $25m{s^{ - 1}}$takes a U-turn in 5 seconds, without changing its speed. The average acceleration during these 5 seconds is:
A) $5m{s^{ - 2}}$
B) $10m{s^{ - 2}}$
C) $2.5m{s^{ - 2}}$
D) $7.5m{s^{ - 2}}$

Answer 1

Recall that acceleration is the rate of change of velocity with time. It has both magnitude and direction. So it is a vector quantity. The direction of the acceleration of an object can be determined if the net force acting on the object is known.

Complete step by step solution:
Step I: Given that the initial velocity of the car is ${v_{initial}} = 25m/s$
Since it takes a U-turn, the speed of the car is not changed, so final velocity will be the same, but it will be in the opposite direction.
${v_{final}} = - 25m/s$

Step II: The formula of acceleration is written as
$a = \dfrac{{\Delta v}}{{\Delta t}}$
Where $\Delta v$is the change in velocity
$\Delta t$is the time$= 5\sec$

Step III: The change in velocity is written as
$\Delta v = {v_{final}} - {v_{initial}}$
$\Delta v = - 25 - 25$
$\Delta v = - 50m/s$
The negative sign shows that the direction of the car when it takes U-turn, is opposite. But while calculating the value of acceleration, the negative sign should not be used. Because magnitude can not be negative.

Step IV: Substitute the value of velocity and time in the formula and find value of acceleration,
$a = \dfrac{{50}}{5}$
$a = 10m{s^{ - 2}}$

Step V: The average acceleration of the car during these 5 sec is = $10m{s^{ - 2}}.$

Hence Option (B) is the right answer.

Note: It is to be noted that when the object is moving in the direction of velocity, it is known as positive acceleration. The speed of the object increases in positive acceleration. But when the object is moving in an opposite direction to that of velocity, it is known as negative acceleration or deceleration. There is another word used for deceleration. It is known as retardation.