Question

A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the cars motion, the eastward component of the cars velocity is given by vx(t) = (0.930 m / s³)t² . What is the acceleration of the car when vₓ= 13.9 m/s?

Answer 1

To calculate the acceleration of the car when vₓ = 13.9 m/s, solve for the time t in the equation vx(t) = (0.930 m/s³)t² to get t, then differentiate the velocity equation and substitute the value of t to find the acceleration.

Step-by-step explanation:

The student is asking about the acceleration of a race car based on the given velocity-time relationship. The eastward component of the car's velocity is described by the equation vx(t) = (0.930 m / s3)t2. To find the acceleration at the moment when vx = 13.9 m/s, we can start by calculating the time t at which the velocity reaches this value using the given equation, and then differentiate the velocity equation to get acceleration as a function of time.

To find the time t when vx = 13.9 m/s, we solve the equation 13.9 = (0.930)t2. Solving for t gives t = \sqrt{\frac{13.9}{0.930}}. Once we have the value of t, we can find the instantaneous acceleration by differentiating the velocity equation, resulting in a(t) = 2 * (0.930) * t. Plugging in the value of t will give us the acceleration at the moment when the velocity is 13.9 m/s.