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Is it true that the first car travelled, travelled farther after the brakes were applied when a driver of a car travelling at $52 km / h$ applies brakes and accelerates uniformly in the opposite direction and the car stops in $5 s$ , while another driver going at $3 km / h$ in another car applies his brakes slowly and stops in $10 s$ ?

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True

False

answer is A.

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Detailed Solution

The above statement is true.
Given: initial speed of first car

(u) = 52 km / h

= 52 \times \frac{5}{18}

= 14.44 m / s

, final speed of the first car

(v) = 0,

time taken

(t) = 5 s

, initial speed of second car

(U) = 3 km / h

= 3 \times \frac{5}{18}

= 0.83 m / s

,
final speed of the second car

(V) = 0

,
time taken

(T) = 10 s

Distance travelled by the first car = Area under curve PQ
or,

\frac{1}{2} \times 5 \times 14.44

= 36.1 m

Distance travelled by the second car = Area under curve RS
or,

\frac{1}{2} \times 10 \times 0.83

= 4.15 m

Therefore, the first car travelled more distance than the second car.

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