The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 3 sin(πt) + 4 cos(πt), where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average velocity during each time period. (i) [1, 2] cm/s (ii) [1, 1.1] cm/s (iii) [1, 1.01] cm/s (iv) [1, 1.001] cm/s (b) Estimate the instantaneous velocity of the particle when t = 1. cm/s

Guest Apr 23, 2020

#1**+1 **

plug in t= 1 to find s = displacment = -4 cm

@ t = 2 s = +4

So in one second from 1 to 2 displacement chages by 8 average velocity is 8 cm / 1 sec = 8 cm/sec

do similar for the other time frames

b. since it asks for an estimate.....try to estimate the slope of the equation at t= 1

it is negative

it is NEARLY a straight line between t = .5 (value ~ 3) to t = 1 (value = -4)

slope = ( 3 - - 4) / (.5 - 1) = -7/.5 = -14

approx -14 cm/sec

Here is a desmos graph which ma help you ....

https://www.desmos.com/calculator/fkg8uqs8z0

ElectricPavlov Apr 23, 2020