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
This question is dealing with velocity, acceleration and time of motion.
Acceleration is; aₓ = 7.54 m/s²
We are told that the eastward component of the car's velocity is;
uₓ(t) = (0.980 m/s³) t²
Now, from calculus differentiation in maths, we know that with respect to time, the derivative of velocity is equal to the acceleration.
Thus;
aₓ(t) = du/dt = 2t(0.980 m/s³)
aₓ(t) = 1.96t m/s³
We w ant to find the acceleration of the car when velocity is; uₓ = 14.5 m/s. Let us find the time first and then plug the value into the acceleration equation.
Thus;
14.5 m/s = (0.980 m/s³) t²
14.5/0.98 = t²
t = 3.85 s
Putting 3.85 for t in the acceleration equation to get;
aₓ = (1.96 m/s³) (3.85 s)
aₓ = 7.54 m/s²
Read more at; brainly.com/question/2140807
