Verified answer

We need a velocity equation.

The position function gives us an answer in terms of meters (or feet).

The velocityfunction gives us an answer in terms of meters (or feet) per second.

We can get the velocity by taking the derivative of the position function with respect to time.

v(t) = d/dt s(t)

= d/dt t + d/dt sin ( π / t )

= 1 + d/dt ( π / t ) * cos ( π / t )

= 1 + π d/dt (t^-1) * cos ( π / t )

= 1 + π (-1) (t^-2) * cos ( π / t )

= 1 - π*cos ( π / t ) / t²

Now evaluate v(t) at t = 3:

v(3) = 1 - π*cos ( π / 3 ) / 3²

= 1 - [π*(1/2) ] / 9

= 1 - π/18

~= 1.7924444

So what would happen if we took the derivative of the velocity function with respect to time? We'd get the acceleration function which has units of meters (or feet) per second². That's m/s².

v(t) = ds/dt. so differentiate s with respect to t and sub in 3 into the answer.