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A child having a mass of $35 kg$ sitting on a trolley of mass $5 kg$ . The trolley is moved with an initial velocity of $4 m / s$ by applying a force. The trolley came to rest after travelling a distance of $16 m .$ Find the work done on the trolley.

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160 J

320 J

640 J

1280 J

answer is B.

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Detailed Solution

The amount of work done on the trolley is

320 Joules

.
Given, the initial velocity of the trolley,

u = 4 m / s

Final velocity of the trolley,

v = 0 m / s

Distance travelled by the trolley,

s = 16 m

From third equation of the motion,

{\Rightarrow v}^{2} - u^{2} = 2 as

Acceleration of the trolley is given by,

\Rightarrow a = \frac{(v^{2} -^{} u^{2})}{2 s}

\Rightarrow a = \frac{0 - (4)^{2}}{2 \times 16}

\Rightarrow a = \frac{16}{2 \times 16}

\Rightarrow a = - 0.5 m / s^{2}

Work done on the trolley by the force

\Rightarrow W = Fs

\Rightarrow W = mas

\Rightarrow W = (35 + 5) \times (0.5) \times 16

\Rightarrow W = 20 \times 16

\Rightarrow W = 320 J

Therefore, the amount of work done on the trolley is

320 Joules

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