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

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Answer 1 · 2018-07-20T01:13:02

The speed of the object at #t=8# is approximately #s=120.8 m/s#

I will be rounding to the nearest decimal place for convenience

Speed is equal to distance multiplied by time, #s=dt#

First, you want to find the position of the object at #t=8# by plugging in #8# for #t# in the given equation and solve

#p(8)=2(8)-sin((8pi)/3)#
#p(8)=16-sqrt3/2#

#p(8)=15.1#

Assuming that #t# is measured in seconds and distance (#d#)is measured in meters, plug into the speed formula

#s=dt#

#s=15.1m*8s#

#s=120.8 m/s#