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joja [24]
3 years ago
11

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.
Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
4 0

Answer:

<em>V(t) = π(4cos πt -5sinπt) cm</em>

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)

<em>Hence the average velocity of the body during each time is expressed as </em>

<em>V(t) = π(4cos πt -5sinπt) cm</em>

<em></em>

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