Question

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 2 t plus 2. Find the instantaneous velocity when t equals 6. What expression can be used to find the instantaneous velocity at the given​ time?

Answer 1

Answer:

v(6) = 62

At any given time: v(t) = 10t + 2

Step-by-step explanation:

The equation that describes the position of the object is:

$s(t) =5t^2+2t+2$

The instantaneous velocity at any given time, v(t), is the derivate of the position expression:

$\frac{ds(t)}{dt}=v(t) =10t+2$

For t = 6, the instantaneous velocity is:

$v(6) =10*6+2\\v(6) = 62$

The instantaneous velocity when t=6 is v(6) = 62 units of distance/units of time.