Question

A ball slides on a horizontal surface with velocity of $0.5\,m{s^{ - 1}}.$ Due to friction, the ball is decelerating at the rate of $0.05\,m{s^{ - 2}}$ ,calculate the time taken by the ball to stop.

Answer 1

Hint: In order to solve this question, we should know about basic difference between acceleration and deceleration, when a body has acceleration which is positive means velocity of body is increasing its called simple acceleration while when a body has negative acceleration which means the velocity is continuously decreasing then it is called deceleration. Here we will use the given deceleration as negative acceleration of the ball and then use Newton's equation of motion to find time taken by the ball to stop.

Formula used:
If $v$ is the final velocity of the body and $u$ is the initial velocity with acceleration a and time t then, newton equation of motion is written as,
$v = u + at$

Complete step by step answer:
According to the question we have given that,
Initial velocity of ball,$u = 0.5\,m{s^{ - 1}}$.
Final velocity of the ball in order to come at rest, $v = 0$.
Negative acceleration because the body is decelerating due to friction, $a = - 0.05\,m{s^{ - 2}}$.
Let us assume ball takes ‘t’ time to come at rest then using formula,
$v = u + at$
Put the value of parameters we get,
$0 = 0.5 - 0.05t$
$\Rightarrow t = \dfrac{{50}}{5}$
$\therefore t = 10\,s$

Hence the ball will take time off $t = 10\,s$ to come to rest.

Note: It should be remembered that, when a body is moving on a surface and friction force which acts in direction opposite to that of motion on the point of contact between surface and the body, then friction force always tries to oppose the motion that’s why the acceleration is negative means velocity of body continuously gets decreased and body came to rest due to frictional force.