The position of a particle moving on X-axis is given by `x =At^(2) + Bt + C` The numerical values of A, B and C are 7, -2 and 5 respectively and SI units are used. Find
(a) The velocity of the particle at t= 5
(b) The acceleration of the particle at t =5
(c ) The average velocity during the interval t = 0 to t = 5
(d) The average acceleration during the interval t = 0 to t = 5

Explanation

To solve the problem step by step, we will analyze the motion of the particle given by the equation \( x = At^2 + Bt + C \) with the values \( A = 7 \), \( B = -2 \), and \( C = 5 \).

### Step 1: Find the velocity of the particle at \( t = 5 \)

1. **Differentiate the position function** to find the velocity function:
\[ v(t) = \frac{dx}{dt} = \frac{d}{dt}(At^2 + Bt + C) = 2At + B \]
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