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 the measured in seconds.
a) find the average velocity for the 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

Question

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 the measured in seconds.
a) find the average velocity for the 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

anonymous · Answer

instantaneous velocity
$$v=2\pi \cos \pi t-3\pi \sin \pi t $$
av velocity
$$v_{av}=\frac{\int\limits_{t1}^{t2}v dt}{t2-t1}$$