# A car moving rectilinearly with acceleration

1 vote
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A car starts moving rectilinearly first with acceleration $a= 5 m/s^2$( the initial velocity is equal to zero ) then uniformly and finally be decelerating at the same rate$a$ and comes to stop. The total time of the motion equal to $25 s$ the average velocity during that time is equal to 72 km/h . How long does the car move uniformly ?

I tried this by thinking that if car has constant acceleration first then its average velocity would have been same throughout the middle journey where it has uniform velocity and that is 20 m/s
so if it takes 4 seconds to accelerate and decelerate then 25 -8 = 17 sec

But given answer is 15 s . How ?

The average velocity over the whole journey is 20 m/s. You have assumed that the maximum velocity is 20 m/s, which is not correct.

1 vote

The average speed over the whole journey is 20 m/s so the total distance covered is 20 x 25 = 500 m.

Suppose the acceleration phase lasts time t. Then the maximum speed is v=5t. The total distance covered is the area of the trapezium with parallel sides of 25 and 25-2t separated by distance v. So
$\frac12 v(25+25-2t)=5t(25-t)=500$
$t(25-t)=100$.

By inspection t=5 s. So the time spent at maximum speed is 25-2t = 15 s.

answered Jul 29, 2017 by (27,948 points)
selected Jul 29, 2017
ohk I misunderstood that average speed was given for that uniform velocity time period itself