The position of an object moving along a line is given by #p(t) = 4t - sin(( pi )/3t) #. What is the speed of the object at #t = 8 #?

1 Answer
Mar 27, 2017

Answer:

#4.52ms^-1#

Explanation:

In this case,
we know that,

Instantaneous speed=#dx/dt#
where "dx" denotes the position of an object at a particular moment (instant) in time and "dt" denotes the time interval.

Now,by using this formula,we have to differentiate the above equation
#p(t)=4t-sin(π/3t)#
#=>(dp(t))/dt=4(dt/dt)-(dsin(π/3t))/dt#
#=>(dp(t))/dt=4-cos(π/3t).(π/3t)##[(dsinx)/dt=cosx]#
At t=8,

#=>(dp(t))/dt=4-cos(π/3*8)(π/3) #
#=>(dp(t))/dt=4--0.52=4.52#

So the answer will be #4.52ms^-1#