The velocity of an object as a function of time is given by v = (12.5t − 7.2t²) + (4.3t³) .What is its acceleration as a function of time? A)a = (12.5 − 14.4t) + (12.9t²) B)a = (−7.2) + (4.3t) C)a = (5.3t) + (12.9t²) D)a = (−7.2) + (8.6t) E)a = (−14.4t) + (4.3t²)

Question

Quizplus · Accepted Answer

To find the acceleration as a function of time, we need to take the derivative of velocity with respect to time:

a = dv/dt

a = d/dt [ (12.5t − 7.2t^2) + (4.3t) ]

a = (12.5 − 14.4t) + 4.3

Simplifying the expression, we get:

a = (12.5 − 14.4t) + 4.3

a = 5.3t − 13.2

Therefore, the correct choice is A.

The Velocity of an Object as a Function of Time