A car traveling at a constant speed of $30 m / s$ passes a highway patrol car, which is at rest. The police officer accelerates at a constant rate of $3 m / s^{2}$ and maintains this rate of acceleration until he pulls next to the speeding car. Assume that the police car starts to move at the moment the speeder passes the police car. What is the time required for the police officer to catch the speeder?

20 s

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30 s

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40 s

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50 s

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Solution

The correct option is A $20 s$
Let the time taken be t seconds
Distance travelled by speeder= $30 \times t$
Distance travelled by police in the same time= $\frac{1}{2} \times a \times t^{2} = 1.5 \times t^{2}$
Equating the distance travelled by speeder and police, we get
$\Rightarrow t = 20 s$

Hence correct answer is option $A$

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The correct option is A 20sLet the time taken be t secondsDistance travelled by speeder=30×tDistance travelled by police in the same time=12×a×t2=1.5×t2Equating the distance travelled by speeder and police, we get⇒t=20sHence correct answer is option A