The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 4 sin πt + 5 cos πt, where t is measured in seconds. (Round your answers to two decimal places.)(a) Find the average velocity during each time period.

V(t) = π(4cos πt -5sinπt) cm

Step-by-step explanation:

Given the displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 4 sin πt + 5 cos πt, where t is measured in seconds, the average velocity of the body will be expressed as the change in displacement of thee particle with respect to time.

This is expressed mathematically as V = ds/dt

Differentiate the displacement function to get the velocity V

V = 4πcos πt + (-5πsin πt)

open the parenthesis

V = 4πcos πt - 5πsin πt

bring out the common factor

V = π(4cos πt -5sinπt)

Hence the average velocity of the body during each time is expressed as

V(t) = π(4cos πt -5sinπt) cm