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Starting from a stationary position, Rahul paddles his bicycle to attain a velocity of $6 m / s$ in $30 s$ . Then he applies brakes such that the velocity of the bicycle comes down to $4 m / s$ in the next $5 s$ .

The acceleration of the bicycle in both cases will be__

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0.2 m / s^{2}; - 0.4 m / s^{2}

0.3 m / s^{2}; + 0.4 m / s^{2}

0.2 m / s^{2}; - 0.3 m / s^{2}

0.2 m / s^{2}; + 0.2 m / s^{2}

answer is A.

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Detailed Solution

The acceleration of the bicycle in both the cases will be

0.2 m / s^{2} and 0.4 m / s^{2}

For first case:

Initial velocity (u_{1}) = 0 m / s

Final velocity (v_{1}) = 60 m / s

Time (t_{1}) = 30 \sec

v = u + at

[using the equation of motion]

\Rightarrow 6 = 0 + a \times 30

\Rightarrow 6 = 30 a

\Rightarrow a = 0.2 m / s

For second case:

Initial velocity (u_{2}) = 6 m / s

Final velocity (v_{2}) = 4 m / s

Time taken (t_{2}) = 5 \sec

v = u + at

[using the equation of motion]

\Rightarrow 4 = 6 + a \times 5

\Rightarrow 4 - 6 = 5 a

\Rightarrow - 2 = 5 a

\Rightarrow a = - 0.4 m / s^{2}

A negative acceleration indicates that the acceleration is in the direction opposite to the motion.

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