The position of an object moving along a line is given by #p(t) = t - tsin(( pi )/3t) #. What is the speed of the object at #t = 1 #?

1 Answer
Douglas K.
Apr 28, 2017

#p'(1) ~~ -0.389# distance units/time units

Explanation:

The speed of the object at any given time, #t_1#, is the first derivative, #p'(t)#, evaluated that time.

Compute the first derivative:

#p'(t) = 1 - sin(pi/3t)-pi/3tcos(pi/3t)# distance units/time units

Evaluate at t = 1:

#p'(1) ~~ -0.389# distance units/time units

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