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. (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.
cm/s

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 πt + 3 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.
 cm/s

anonymous · Answer

average velocity = ds/dt

=d/dt ( 2 sin πt + 3 cos πt)

= 2π cos πt - 3πsin πt


if u substitute the values of time interval as upper limit and lower limit u will get the average velocity