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velocity of a particle varies with time as v=t^2-t-2. average speed of the particle in time interval from t=0 to t=4sec?

velocity of a particle varies with time as v=t^2-t-2. average speed of the particle in time interval from t=0 to t=4sec?

Grade:12

1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear student,

For average speed we need to know the total distance travelled by particle in 4 seconds.

v=t^2-t-2=(t-2)(t+1)

velocity of body is zero at t=2 seconds and the velocity reverses its direction.

Distance travelled upto 2 seconds=\int_0^2(t^2-t-2)dt=\dfrac{2^3}{3}-\dfrac{2^2}{2}-2(2)=\left|\dfrac{8}{3}-6\right|=6-\dfrac{8}{3}

Distance travelled from t=2 to t=4 =

\int_2^4(t^2-t-2)dt=\dfrac{4^3-2^3}{3}-\dfrac{4^2-2^2}{2}-2(4-2)=\dfrac{56}{3}-10

Hence total distance travelled by body=12m

Hence average speed=3m/s

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