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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

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the displacement (in centimeter) of a prarticle moving back and fort.pdf

  • 1. 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