A particle has a position function of rt=(28 meters) coswt i + t j where w=0.125

Question

A particle has a position function of

rt=(28 meters) coswt i + t j

where w=0.125 s-1 , and t is measured in seconds.

a) Calculate the position at time t = 2.0 s (note that your calculator should be set to radians for this)

b) By differentiation of the position function with respect to time, derive the velocity function.

c) Calculate the velocity vector at time t = 2.0 s

d) Calculate the speed at time t = 2.0 seconds.

e) If the particle has a mass of 4.0×10^2 kg, calculate the kinetic energy in joules.

f) Use a spreadsheet to calculate the position of the particle for time t = 0 to time t = 50 s in 1 second increments. Show these coordinates on a scatter plot, which represents the trajectory of the particle. Include the scatter plot in your solution. (cutting and pasting it into this document is recommended)

Explanation / Answer

rt = (28 meters) coswt

w = 0.125

rt = (28 meters) cos(0.125)t

a)

at t = 2 sec

rt = (28 meters) cos(0.125)2

rt = 27.13 m

b)

taking derivative of the above equation both side

V = 28 d(Cos0.125t)/dt

V = 28 (0.125) (-Sin(0.125t))

V = -3.5 Sin(0.125t)

c)

at t = 2

V = -3.5 Sin(0.125 x 2)

V = -3.5 Sin(0.25)

d)

at t = 2

V = -3.5 Sin(0.125 x 2)

V = - 0.866 m/s

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