A marble rolling on a smooth floor has an initial velocity of $0.4m/s$ . If the floor offers a retardation of $0.02 {m s}^{- 2}$ , calculate the time it will take to come to rest.

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Solution

Given Data:
The initial velocity of marble is, $u = 0.4m/s$
And the retardation is, $a = - 0.02 m s^{- 2}$
['a' is negative because it is regarding]

Now by first equation of motion
$v=u+at$
where u is initial velocity,v is final velocity a is acceleration and t is time.
Putting the values in the equation,we get

$0=0.4+(-0.02)t$ [final velocity is 0 because body comes to rest.]
So,
$0.02t=0.4$
$t = \frac{0.4}{0.02} = 20 s e c$
So required time is $t = 20s.$

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A marble rolling on a smooth floor has an initial velocity of 0.4m/s . If the floor offers a retardation of 0.02ms−2 , calculate the time it will take to come to rest.

A marble rolling on a smooth floor has an initial velocity of $0.4m/s$ . If the floor offers a retardation of $0.02 {m s}^{- 2}$ , calculate the time it will take to come to rest.