The position of an object moving along a line is given by #p(t) = 3t - tsin(( pi )/8t) #. What is the speed of the object at #t = 2 #?

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Answer 1 · 2018-02-22T14:07:12

The speed is #=1.74ms^-1#

Reminder :

The derivative of a product

#(uv)'=u'v-uv'#

#(tsin(pi/8t))'=1*sin(pi/8t)+pi/8tcos(pi/8t)#

The position of the object is

#p(t)=3t-tsin(pi/8t)#

The speed of the object is the derivative of the position

#v(t)=p'(t)=3-sin(pi/8t)-pi/8tcos(pi/8t)#

When #t=2#

#v(2)=3-sin(pi/4)-pi/4cos(pi/4)#

#=3-sqrt2/2-sqrt2/8pi#

#=1.74ms^-1#