- 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.

^{2}-u

^{2}=2as

Now, when accelerating, v = v ; u = 0; a = 5m/s

^{2}.

v

^{2}-0

^{2}=2(5)s

Now when decelrating, u = v; v = 0, a = -10 m/s

^{2}

0

^{2}-v

^{2}=2(-10)s

Combining both the distances should be equal to 1500m.

So, v

^{2}/20+v

^{2}/10=1500

3v

^{2}/20=1500

3v

^{2}=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.

**
**