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

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Answer 1 · 2017-04-28T09:56:59

The speed is #=0.63ms^-1#

We need

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

The speed is the derivative of the position

#p(t)=2t-tsin(pi/8t)#

Therefore,

#v(t)=2-(sin(pi/8t)+t*pi/8cos(pi/8t))#

#=2-sin(pi/8t)-(tpi)/8cos(pi/8t)#

When #t=3#

#v(3)=2-sin(3/8pi)-(3/8pi)cos(3/8pi)#

#=2-0.92-0.45#

#=0.63ms^-1#