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
Rajarshi B.
Mar 27, 2017

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

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