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 υx(t)=(0.980m/s3)t2.
What is the acceleration of the car when υx = 14.5 m/s ?

Answer 1

Answer:

7.54 m/s²

Explanation:

uₓ(t) = (0.980 m/s³) t²

Acceleration is the derivative of velocity with respect to time.

aₓ(t) = 2 (0.980 m/s³) t

aₓ(t) = (1.96 m/s³) t

When uₓ = 14.5 m/s, the time is:

14.5 m/s = (0.980 m/s³) t²

t = 3.85 s

Plugging into acceleration equation:

aₓ = (1.96 m/s³) (3.85 s)

aₓ = 7.54 m/s²