A particle starts from rest and moved in a straight line the velocity of the particle at time t after start is v m/s where v= 0.01t^3 +0.22t^2 -0.4tv=0.01t3+0.22t20.4t Find the time at which the acceleration of the particle is greatest?

1 Answer
May 16, 2018

See below.

Explanation:

We have the velocity function:

v=0.01t^3+0.22t-0.4tv=0.01t3+0.22t0.4t

"acceleration"=("change in velocity")/("time")acceleration=change in velocitytime

Hence:

a=(dv)/(dt)a=dvdt

a=(dv)/(dt)(0.01t^3+0.22t-0.4t)=0.03t^2+0.44t-0.4a=dvdt(0.01t3+0.22t0.4t)=0.03t2+0.44t0.4

This is the function of acceleration.

We need to find maximum value of this. Using the derivative of this and equating to zero will identify local maxima and minima.

(da)/(dt)(0.03t^2+.44t-0.4)=0.06t+0.44dadt(0.03t2+.44t0.4)=0.06t+0.44

0.06t+0.44=0=>t=-7.33s0.06t+0.44=0t=7.33s

As pointed out in the comments, there must be an error in the function.