Answer:
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
