Calculating Stopping Time for a Body under Constant Retarding Force

Question:

A constant retarding force of 50 N is applied to a body of mass 20 Kg moving initially with a speed of 15 ms^-1 .How long does the body take to stop?

Solution: Stopping time calculation:

Calculating the acceleration:

$${Acceleration =\frac{Force}{Mass}}$$

$${Acceleration =\frac {50 \ N}{20 \ Kg}}$$

$${Acceleration= 2.5 \ \frac{m}{s^2}}$$

Retardation:

Retardation is -2.5 ms^-2

Since the force is retarding, the acceleration is negative.

Time taken to stop:

$${v=u+at}$$

Initial velocity u =15 ms^-1

Final velocity v = 0

Acceleration a = -2.5 ms^-2 ( it is retarding}

Time taken =?

$${t=\frac{v-u}{a}}$$

$${t=\frac{0-15}{-2.5}}$$

$${t=6 sec}$$

Conclusion:

The body takes 6 seconds to stop under the action of a constant retarding force of 50 N.