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Grade 12AIPMT

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?

Jay

8 Years agoGrade 12

1 Answer

Eshan

8 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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