The acceleration of a motorcycle is given by `a_x(t)=At-Bt^2`, where `A=1.50ms^-3` and `B=0.120ms^-4`. The motorcycle is at rest at the origin at time `t=0`.
a. Find its position and velocity as funcitons of time.
b. Calculate the maximum velocity it attains.

Explanation

To solve the problem step by step, we will follow the outlined approach in the video transcript.

### Given:
- Acceleration: \( a_x(t) = At - Bt^2 \)
- Constants: \( A = 1.50 \, \text{m/s}^3 \), \( B = 0.120 \, \text{m/s}^4 \)
- Initial conditions: At \( t = 0 \), \( x(0) = 0 \) and \( v(0) = 0 \)

### Part a: Find the position and velocity as functions of time.
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