Question

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`?

Answer 1

`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`