Question

A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the car's motion, the eastward component of the car's velocity is given by vx(t)=(0.950m/s³)t² . What is the acceleration of the car when vx = 16.3 m/s ? Express your answer with the appropriate units.

Answer 1

The acceleration of the race car when vx = 16.3 m/s is approximately 8.19 m/s².

Step-by-step explanation:

The acceleration of the race car can be found by taking the derivative of the velocity function with respect to time. In this case, the velocity function is vx(t) = (0.950m/s³)t². Taking the derivative of this function gives the acceleration function ax(t) = 2(0.950m/s³)t. To find the acceleration when vx = 16.3 m/s, we can plug in this value into the velocity function and solve for t:

16.3 = (0.950m/s³)t²

t² = 16.3 / 0.950 = 17.16

t = √17.16 ≈ 4.14 s

Now, we can plug this value of t into the acceleration function to find the acceleration:

ax(4.14) = 2(0.950m/s³)(4.14) ≈ 8.19 m/s²