The position of a particle varies with time according to the relation `x=3t^(2)+5t^(3)+7t`, where x is in m and t is in s. Find
(i) Displacement during time interval t = 1 s to t = 3 s.
(ii) Average velocity during time interval 0 - 5 s.
(iii) Instantaneous velocity at t = 0 and t = 5 s.
(iv) Average acceleration during time interval 0 - 5 s.
(v) Acceleration at t = 0 and t = 5 s.

Explanation

To solve the problem step by step, we will follow the instructions given in the question.

### Given:
The position of a particle is defined by the equation:
\[ x(t) = 3t^2 + 5t^3 + 7t \]
where \( x \) is in meters and \( t \) is in seconds.

### (i) Displacement during the time interval \( t = 1 \, \text{s} \) to \( t = 3 \, \text{s} \)
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