The position of an object moving along a line is given by #p(t) = 4t - sin(( pi )/4t) #. What is the speed of the object at #t = 3 #?

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Answer 1 · 2017-06-19T05:40:59

The speed is #=4.56ms^-1#

The speed is the derivative of the position.

#p(t)=4t-sin(pi/4t)#

#v(t)=p'(t)=(4t)'-(sin(pi/4t))'#

#=4-pi/4cos(pi/4t)#

When #t=4#, we have

#v(4)=4-pi/4cos(3/4pi)#

#=4+0.56#

#=4.56#