if position vector is `vecr =4t^4−6t^3+3t^2+4tm ` find the acceleration at t=2 sec.

Explanation

Assigning usual symbols `vec(v)_(m), vec(v)_(r)` and `vec(v)_(r//m)` to velocity of man, velocity of rain and velocity of rain relative to man, we can express their relationship by the following equation
`vec(v)_(r)=vec(v)_(m)+vec(v)_(r//m)`
The above equation suggests that a standstill man observes velocity `vec(v)_(r)` of rain relative to the ground and while he is moving with velocity `vec(v)_(m)`, he observes velocity of rain relative to himself `vec(v)_(r//m)` for optimum proection from tain. According to these facts, directions of the velocity vectors are shown in the adjoining figure.
The addition of velocity vectors is represented according to the above equation is also represented. From the figure we have
`v_(r)=v_(m) tan 37^(@)=3 km//h`