A car starts from rest and accelerates at uniform rate of 5 $m s^{- 2}$ for some time. It then moves with constant speed for some time, retards at the same uniform rate of 5 $m s^{- 2}$ and comes to rest. Total time for the journey is 25 s and average speed for the journey is 20 m/s. How long does the car move with constant speed?

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10 s

12 s

18 s

15 s

answer is C.

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Detailed Solution

As it has average velocity 20m/s and travels for 25 sec, the total distance travelled is 25 x20=500m. Assuming journey is with constant acceleration and retardation for time t (for both cases same magnitude and same initial or final velocity)

So distance travelled during this time= $2 \times \frac{1}{2} a t^{2}$ and remaining time $(25 - 2 t)$ with maximum velocity i.e. “at” then $2 \times \frac{1}{2} a t^{2} + (25 - 2 t) a t = 500 a t^{2} + 25 a t - 2 a t^{2} = 500 h e r e a = 5 m / s^{2} 5 t^{2} + 125 t - 10 t^{2} = 500 o r, t^{2} - 25 t + 100 = 0 S o l v i n g, w e g e t t = 5 o r 20 20 i s n o t p o s s i b l e a s t o t a l t i m e i s m o r e t h a n 2 t T i m e f o r c o n s \tan t v e l o c i t y i s 25 - 10 = 15$