Question

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.)
Find the average velocity during each time period.
1,2
1,1.1
1,1.01
1,1.001???

Answer 1

Velocity is the derivative of displacement with respect to time. Your first step therefore is to differentiate s with respect to t!

Answer 2

so derive the equation??

Answer 3

Yeps. Give it a shot.

Answer 4

omg o.O ive never derived sin or cos before

Answer 5

pi(4cospit)-(5sinpit)?

Answer 6

That's almost right, good job for your first try at sin and cos :) In fact, I suspect it's a typo, or just an oversight that you wrote \(5sin(\pi t\)) instead of \(5\pi sin(\pi t)\)

Answer 7

The rest is correct, including your signs.

Now I'm not entirely sure about the rest of the question. What I can tell you is that sin and cos repeat themselves from 0-2\(\pi\) (one period). Since the question asks about time periods, I'm guessing that you need to find the velocity at 0, and at 2\(\pi\). These would be at t=0, and t=2 respectively. The average would then probably be the sum divided by two (though there may be some calculus that I'm missing).

Answer 8

mmm okay i think i get it. thank you for helping me! could you maybe help me with one more?

Answer 9

i have the same assignment, and we need to plug in the numbers and guess, not differentiate because we havent done that yet in class... but I still cant do it...

Answer 10

did you get it right christaljade?