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A car accelerates from rest at a constant rate of $2 m / s^{2}$ for some time. Then it retards at constant rate of $4 m / s^{2}$ and comes to rest. It remains in motion for 6s.

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Its maximum speed is 8m/s

Its maximum speed is 6 m/s

It travels a total distance of 24m

It travels a total distance of 18m

answer is A, C.

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Detailed Solution

$a_{1} = 2 m / s^{2}; a_{2} = - 4 m / s^{2}$

$v_{0} = a_{1} t_{1} = 2 t_{1}$

$v_{0} = a_{2} t_{2} = 4 t_{2}$

$t_{1} t_{2} = 6$

$\frac{v_{0}}{2} + \frac{v_{0}}{4} = 6$

$∴ v_{0} = 8 m / s$

Total distance travelled

$S = \frac{1}{2} V_{0} t_{1} + \frac{1}{2} V_{0} t_{2}$

$= \frac{1}{2} V_{0} (t_{1} + t_{2})$

$= \frac{1}{2} \times 8 \times 6$

24m

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