the displacement (in centimeter) of a prarticle moving back and forth along a straight line is given by thev equation of motion s =2 sin t +3 cos t, where t is measured in seconds. a) find the average velocity during each time period; i)[1,2] ii) [1,1.1] iii) [1,1.01] iv [1,1.001] Solution s=2sint+3cost average velocity, vav=[s(t2)-s(t1)]/(t2-t1) a) i) s(2)=2sin2+3cos2=3 s(1)=2sin+3cos=-3 vav=[3-(-3)]/(2-1)=6 cm/s ii)s(1.1)=2sin1.1+3cos1.1=-3.471 s(1)=2sin+3cos=-3 vav=[-3.471-(-3)]/(1.1-1)=-4.712 cm/s iii)s(1.01)=2sin1.01+3cos1.01=-3.061 s(1)=2sin+3cos=-3 vav=[-3.061-(-3)]/(1.01-1)=-6.134 cm/s iv)s(1.001)=2sin1.001+3cos1.001=-3.00627 s(1)=2sin+3cos=-3 vav=[-3.00627-(-3)]/(1.001-1)=-6.268 cm/s.