Question

Brenda runs track for Clinton. Her friend said that they could outrun Brenda anytime. Brenda wanted to prove mathematically how fast she was by modeling her position with the function below, where t is measured in seconds. At what time was Brenda's acceleration equal to zero?

A) 0 seconds
B) 1 second
C) 2 seconds
D) 3 seconds

Answer 1

Without the specific function describing Brenda's position, we cannot mathematically determine the time at which her acceleration is zero. The acceleration is found by taking the second derivative of the position function, which in a quadratic function is a constant value.

Step-by-step explanation:

The question asked by Brenda concerns when her acceleration is equal to zero given her position modeled by a function of time, t, where t is measured in seconds. Unfortunately, the function itself is missing from the provided information. To determine when the acceleration is zero, we would need to take the second derivative of the position function, which gives us acceleration, and then set that equal to zero to solve for t.

For example, if Brenda's position as a function of time, x(t), was given by a quadratic equation like x(t) = at2 + bt + c, then the first derivative v(t) = 2at + b represents her velocity, and the second derivative a(t) = 2a represents her acceleration.

In the example provided, the acceleration is constant, 2a, hence if a ≠ 0, her acceleration is never zero. However, if a = 0, the entire motion would have zero acceleration at all times.