The velocity function, in feet per second, is given for a particle moving along a straight line, where t is the time in seconds. Find the displacement of the particle over the given interval.
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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 πt + 3 cos πt, where t is measured in seconds.
(a) Find the average velocity during each time period:
(i) [1, 2]
(ii) (1, 1.1]
The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 3/t2 , where t is measured in seconds. Find the velocity of the particles at times t=a, t=1, t=2, and t=3.
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(πt) + 2 cos(πt), where t is measured in seconds. (Round your answers to two decimal places.)
(a) Find the average velocity during each time period.
(i) [1, 2] cm/s
(ii) [1, 1.1] cm/s
(iii) [1, 1.01] cm/s
(iv) [1,1.001] cm/s
(b) Estimate the instantaneous velocity of the particle when t=1.
