A particle moves in a straight line At time t seconds its ve

A particle moves in a straight line. At time t seconds its velocity is given by v(t) = t2 + 2t - 8 m/s. Find an expression for the displacement s(t) from O at time t given that the initial position is 4 metres from the origin O (in the positive direction). Draw the motion diagram and find the distance travelled in the first 3 seconds.

Solution

s(t)=integration(v(t))
s(t)=t^3/3+t^2-8t
s(t)=4=t^3/3+t^2-8t
t=3.91s
at t=3.91 v(t)=15m/s
v(t)=0 when t=2
t=3.91 to 5.91
moves right
s(t)=-9.333
t=5.91 to 6.91
changes direction
again s(t)=-6.67
total distance =(9.33-6.67)+9.33=15.9m=11.99m