Question

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 4 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
ii) 1,1.1
iii)1,1.01
iv)1, 1.001

Answer 1

Distance:
s = 4sin(πt) + 3
Differentiating with respect to time in order to get velocity,
v = 4cos(πt)
average velocity = (v₁ + v₂)/2
i) v(1) = 4cos(π) = -4
v(2) = 4cos(2π) = 4
Vavg = (4-4)/2 = 0

ii) v(1) = -4
v(1.1) = -3.8
Vavg = (-4 - 3.8)/2 = -3.9 m/s

iii) v(1) = -4
v(1.01) = -3.998
Vavg = (-4 - 3.998)/2 = -3.999 m/s

iv) v(1) = -4
v(1.001) = -3.99998
Vavg = -3.99999 m/s