1. A scooter can produce a maximum acceleration of 5 m/s2. Its brake can produce a maximum retardation of 10 m/s2. Find THE MINIMUM TIME IN WHICH IT STARTS THE REST, COVERS A DISTANCE OF 1.5 km and stops again.

v2-u2=2as
Now, when accelerating, v = v ; u = 0; a = 5m/s2.
v2-02=2(5)s

Now when decelrating, u = v; v = 0, a = -10 m/s2
02-v2=2(-10)s

Combining both the distances should be equal to 1500m.
So, v2/20+v2/10=1500
3v2/20=1500
3v2=30000
v = 100m/s.
So, the minimum time can be found out by:
Acceleration:
v-u=at
=100-0=5t
t = 20 s
Deceleration:
v-u=at
0-100=-10t
t=10s

Total time taken is 30s.

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