Question

The distance an object moves from its starting point is given by the equation s(t) = 3t2 + 4t, where s is given in meters and t is given in seconds. Find the instantaneous rate of change of the object at t = 2

Answer 1

The instantaneous rate of change of the object at t = 2 is 16 m/s.

Step-by-step explanation:

The distance an object moves from its starting point is given by the equation s(t) = 3t² + 4t, where s is given in meters and t is given in seconds. To find the instantaneous rate of change at t = 2, we need to find the derivative of the position function, which gives us the velocity function.

Derivative of s(t) = 3t² + 4t with respect to t:

v(t) = 6t + 4

Substituting t = 2 into the velocity function:

v(2) = 6(2) + 4 = 12 + 4 = 16 m/s

Therefore, the instantaneous rate of change of the object at t = 2 is 16 m/s.