Question

The velocity of a body moving along a straight line follows the law v = 1.25t – 0.125t2 where v is the velocity in m/s at time t second. Find i) the maximum acceleration and ii) the distance moved in 10 seconds.

Answer 1

v= 1.25t - 0.125t²

For i) a = dv/dt = 1.25-0.250t , as the time will increase acceleration will decrease. So at t=0, the value of a will be maximum.

So max value of a=1.25m/s²

ii) s= integration of dv.dt

S = 1.25t²/2 - 0.125t³/3

Putting t=10seconds

S = 1.25×100/2 - 0.125×1000/3

S= 125/6 = 20.88 m