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.