Question

A driver takes 0.20 s to apply the brakes after he sees a need for it. This is called the reaction time of the driver. If he is driving a car at a speed of 54 km/h and the brakes cause a retardation of 6 m/s^2, find the distance travelled by the car after he sees the need to put the brakes on.

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Answer 1

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Answer 2

Given,

Reaction time = 0.20 sec

Speed = 54km/h = 15m/s

To find distance $\bold{({s}_{1})}$

Distance, $({s}_{1})$ = Speed × Time

Distance, $({s}_{1})$= 15 × 0.20

Distance, $({s}_{1})$= 3.0 m.

At the time when brakes are applied,

Initial velocity, u = 54km/h = 15m/s

Final velocity, v = 0

Retardation/deceleration, a = -6m/s^2

Distance $\bold{({s}_{2})}$ when breaks are applied

$\boxed{2a{s}_{2} = {v}^{2} - {u}^{2}}$

$2 \times (-6) \times {s}_{2} = ({0}^{2}) - ({15}^{2}) \\ \implies -12{s}_{2} = -225 \\ \implies {s}_{2} = \dfrac{-225}{-12} = 18.75 m$

To find the distance (s) travelled by car

$s = {s}_{1} + {s}_{2} \\ = 3 + 18.75 \\ = 21.75m$

Therefore, the distance travelled by the car after he sees the need to put the brakes on is 21.75 m