The position of an object moving along a line is given by #p(t) = t - tsin(( pi )/4t) #. What is the speed of the object at #t = 1 #?

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Answer 1 · 2017-05-03T13:25:41

The speed is #=-0.33ms^-1#

The speed is the derivative of the position.

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

#v(t)=p'(t)=1-sin(pi/4t)-pi/4tcos(pi/4t)#

When #t=1#

#v(1)=1-sin(pi/4)-pi/4cos(pi/4)#

#=1-sqrt2/2-pi/4*sqrt2/2#

#=1-0.707-0.555#

#=-0.33#