Suppose the position of an object moving in a straight line is given by s left parenthesis t right parenthesis equals 5 t squared plus 6 t plus 5. Find the instantaneous velocity when t equals 2.

We are given position function s (t) = 5t^2+6t+5.

We need to find the instantaneous velocity at t=2.

We know, the velocity is the rate of change of position over time.

Rate of change of position function would give us velocity function v (t).

Rate of change can be found by taking derivative of the position function.

Taking derivarive of given position function, we get

s' (t) = 10t+6.

That resulted function is velocity function v (t).

Therefore, v (t) = 10t + 6.

In order to find instantaneous velocity at t=2, we need to plug t=2 in above velocity function.

v (2) = 10*2+6 = 20+6

v (2) = 26.

Therefore, the instantaneous velocity when t=2 is 26.