Suppose that the position of a particle at time t seconds is

Suppose that the position of a particle at time t seconds is p(t)=t^3-4t^2 meters to the right of the origin. Find the average velocity of the particle on the interval [1,3].

Solution

position of a particle p(t)=t^3-4t^2 interval [1,3]

Avg Velocity = { p(3) - p(1) }/( 3 -1)

p(3) = 3^3 -4*3^2 = 27 -4*9 = -9

p(1) = 1^3 -4(1)^2 = 1 - 4 = - 3

Avg Velocity = ( -9 -(-3) )/( 3-1) = (-9 +3)/2 = -6/2 = -3 mt/sec