# 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 ?

Mar 27, 2017

$4.52 m {s}^{-} 1$

#### Explanation:

In this case,
we know that,

Instantaneous speed=$\frac{\mathrm{dx}}{\mathrm{dt}}$
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)$\left[\frac{\mathrm{ds} \in x}{\mathrm{dt}} = \cos x\right]$
At t=8,

=>(dp(t))/dt=4-cos(π/3*8)(π/3)
$\implies \frac{\mathrm{dp} \left(t\right)}{\mathrm{dt}} = 4 - - 0.52 = 4.52$

So the answer will be $4.52 m {s}^{-} 1$