Question

a body is moving in a straight line along x- axis. Its distance from the origin is given by the equation x= 5t - t2, where x is in m and t is in s. find the average speed of the body in the interval t=0 and t=2

Answer 1

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Answer 2

Given :

Equation of distance , $x=5t-t^2$ .

To Find :

The average speed of the body in the interval t=0 s and t=2 s .

Solution :

We know , average velocity is :

$v_{avg}=\dfrac{\int\limits^2_0 {v} \, dt }{\int\limits^2_0 \, dt }\\\\v_{avg}=\dfrac{\int\limits^2_0 {(5t-t^2)} \, dt }{\int\limits^2_0 \, dt }\\\\v_{avg}=\dfrac{|\dfrac{5t^2}{2}-\dfrac{t^3}{3} |_0^2}{2}\\\\v_{avg}=\dfrac{(\dfrac{5(2)^2}{2}-\dfrac{2^3}{3})-(\dfrac{5(0)^2}{2}-\dfrac{0^3}{3})}{2}\\\\v_{avg}=\dfrac{\dfrac{5(2)^2}{2}-\dfrac{2^3}{3}}{2}\\\\v_{avg}=3.67\ m/s$

Therefore , the average speed of the body in the interval t=0 and t=2 s is 3.67  m/s .

Learn More :

Kinematics

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