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A biker applies brakes to slow down from a speed of $10 m / s$ to $5 m / s .$ . If the combined mass of the biker and the bike is $150 kg$ , the work done by the brakes is [[1]] $J$

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Detailed Solution

When a biker applies brakes to slow down from a speed of

10 m / s

5 m / s

, and the if the combined mass of the biker and the bike is

150 kg

, the work done by the brakes is

- 5625 J .

Work done in moving a body is equal to the product of force exerted on the body and the distance moved by the body in the direction of force. Mathematically,

W = F \times s

Where

F

is the force exerted and

s

is the displacement of the body in the direction of the force.
Given:
Mass of the body

(m) = 150 kg

Initial velocity

(u) = 10 m / s

Final velocity

(v) = 5 m / s

By work-energy theorem, we know that

Work done (W) = Change in kinetic energy (K . E .)

\Rightarrow W = \frac{1}{2} m v^{2} - \frac{1}{2} m u^{2}

\Rightarrow W = \frac{1}{2} m (v^{2} - u^{2})

\Rightarrow W = \frac{1}{2} \times 150 \times (5^{2} - 10^{2}) J

\Rightarrow W = - 5625 J

The negative sign indicates that the work done is in the opposite direction of the motion.

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