At time t , the displacement of a particle moving in a straight line by `x = - 4t^(2) +2t` . Find the velocity and acceleration a when t = (1/2) s .

Explanation

To solve the problem step by step, we will find the velocity and acceleration of the particle at time \( t = \frac{1}{2} \) seconds, given the displacement function \( x(t) = -4t^2 + 2t \).

### Step 1: Find the Velocity
The velocity \( v \) of a particle is defined as the rate of change of displacement with respect to time. Mathematically, it is given by:
\[ v = \frac{dx}{dt} \]
Given the displacement function:
...