The acceleration of a particle is given by a (t)=(3.00 `m//s^(2)-(2.00 m/s^(3))`)t. (a) Find the initial speed `v_(0)` such that the particle will have the same x -coordinate at t =5.00 as it had at t=0. (b)What will be the velocity at t =5.00s?

Explanation

To solve the problem step by step, we will break it down into parts (a) and (b) as specified in the question.

### Given:
The acceleration of the particle is given by:
\[ a(t) = 3.00 \, \text{m/s}^2 - (2.00 \, \text{m/s}^3) t \]

### Part (a): Find the initial speed \( v_0 \) such that the particle will have the same x-coordinate at \( t = 5.00 \) s as it had at \( t = 0 \).

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