Question

A car start moving with a intitial velocity 20 m/ and with a uniform retardation. It comes to rest after 5.0s. Find the distance travelled by the car in these 5 s.

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Answer 1

GIVEN:

Initial Velocity of the Car (u) = 20 m/s

Final Velocity of the Car (v) = 0 m/s [As the Car Decelerates Uniformly and comes to Rest]

Time taken by the Car to come to Rest = 5 Seconds

TO FIND:

The Distance Travelled by the Car (s)

Acceleration of the Car (a)

SOLUTION:

At First, we've to Find the Acceleration of the Car :-

Using the Equation, $v = u + at$, we get the Acceleration of the Car as -

$=> 0 = 20 + 5a\\\\=> -20 = 5a\\\\=>\frac{-20}{5} = a\\\\Therefore,\:a = -4 ms^{-2}$

∴ The Acceleration of the Car is $-4ms^{-2}$.

Now, we can find the Distance Travelled by the Car till it came to Rest :-

Using the Equation $v^2 = u^2 + 2as$, we get the Distance of the Car as -

$=> 0^2 = 20^2 + 2(-4)s\\\\=> 0^2 = 20^2 -8s\\\\=> 0 = 400 - 8s\\\\=> 0 - 400 = -8s\\\\=> -400 = -8s\\\\Therefore,\:s = \frac{-400}{-8} = 50$

CONCLUSION:

∴ The Distance Travelled by the Car till it came to Rest in 5 Seconds is 50m