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
+36916 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
