A particle is moving along the x-axis with an acceleration a = 2x where a is in `ms^(–2) and x` is in metre. If the particle starts from rest at x=1 m, find its velocity when it reaches the position x = 3.

Options

A. 8 m/s
B. 16 m/s
C. 4 m/s
D. 0 m/s

Explanation

To solve the problem step by step, we will use the relationship between acceleration, velocity, and displacement. The given acceleration is \( a = 2x \).

### Step 1: Write the relationship between acceleration, velocity, and displacement
We know that acceleration \( a \) can be expressed as:
\[ a = v \frac{dv}{dx} \]
where \( v \) is the velocity and \( x \) is the displacement.
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