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A runner has to cover a total run of $100 m$ . She increases her speed from rest under a uniform acceleration of $1 m / s^{2}$ up to three quarters and she completed last quarters at uniform speed. The time to travel the 2nd half will be

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3.25 s

4.29 s

5.25 s

Cannot say

answer is B.

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Detailed Solution

A runner has to cover a total run of

100 m

. She increases her speed from rest under a uniform acceleration of

1 m / s^{2}

up to three quarters and she completed last quarters at uniform speed. The time to travel the 2nd half will be

4.29 s

.
For three quarters distance

(s) = 75 m

time

t = ?

Acceleration

(a) = 1 m / s^{2}

Initial velocity

(u) = 0

; (as car starts from the rest)
Using the motion formula;

S = ut + \frac{1}{2} a t^{2}

Three quarters:

\Rightarrow 75 = 0 t + \frac{1}{2} 1 t^{2}

t_{1} = 12.25 \sec .

Travel 1st half:
First half distance

(s) = 50 m

Acceleration

(a) = 1 m / s^{2}

Initial velocity

(u) = 0

; (as car starts from the rest)
⇒

50 = 0 t + \frac{1}{2} 1 t^{2}

t = 10 \sec .

Time taken to travel from

50 m

75 m

is =

12.25 - 10

\Rightarrow t = 2.25 s

Speed after 3 quarters, can be calculated using

v = u + at

\Rightarrow v = 0 + 1 \times 12.25

\Rightarrow v = 12.25 m / s

And for remaining

25 m

12.25 m / s

time will be
Using relation

Speed = Distance / time taken

t = s / v

(as the speed is constant after three quarter distance)

\Rightarrow t = 25 / 12.25 s

\Rightarrow t = 2.04 s

(using

Speed = Distance / time taken

)
So total time for 2nd half =

2.25 + 2.04

4.29 s

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