Question

The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 6/t2, where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3.

Answer 1

Answer:

Velocity of the particle at time t = a

        $v(a)=-\frac{12}{a^3}$

Velocity of the particle at time t = 1

         $v(1)=-12m/s$

Velocity of the particle at time t = 2

         $v(2)=-1.5m/s$

Velocity of the particle at time t = 3

          $v(3)=-0.44m/s$

Explanation:

Displacement,

          $s(t)=\frac{6}{t^2}$

Velocity is given by

          $v(t)=\frac{ds}{dt}=\frac{d}{dt}\left ( \frac{6}{t^2}\right )=-\frac{12}{t^3}$

Velocity of the particle at time t = a

        $v(a)=-\frac{12}{a^3}$

Velocity of the particle at time t = 1

         $v(1)=-\frac{12}{1^3}=-12m/s$

Velocity of the particle at time t = 2

         $v(2)=-\frac{12}{2^3}=-1.5m/s$

Velocity of the particle at time t = 3

          $v(3)=-\frac{12}{3^3}=-0.44m/s$