The position of an object moving along a line is given by #p(t) = t-cos(( pi )/2t) #. What is the speed of the object at #t = 2 #?

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Answer 1 · 2017-12-11T11:16:56

The speed is #=1ms^-1#

The speed is the derivative of the position.

#p(t)=t-cos(pi/2t)#

#v(t)=p'(t)=1+pi/2sin(pi/2t)#

Therefore, when #t=2#

#v(2)=1+pi/2sin(pi/2*2)#

#=1+pi/2sin(pi)#

#=1-0#

#=1ms^-1#