The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s= 2 sin pi t + 3 cos pi t, where t is measured in seconds.

Question

(a) Find the average velocity during each time period:

(i)[1,2]
(ii) [1,1.1]
(iii) [1, 1.01]
(iv) [1, 1.001]

(b) Estimate the instantaneous velocity of the particle when t=1.

Can someone please help me with this question, the trig functions have me confused. Please and thanks again.

Answer 1

PUt in the times given, first the final time,then calculate position, then put in the initial time, and calculate position.

avg velocity=(finalposition-initialposition)/timeduration

Answer 2

but how do we treat the cos and sin...just input them like that into the calculator or use radians?

Answer 3

and also for (b) is the answer -2pi

Answer 4

i got -3 for all part a can anyone verify that answer please