A particle of mass `0.5kg` travels in a straight line with a velocity `v=(5x^(5//2))m//s`. How much work is done by the net force during the displacement from `x=0` to `x=2m` ?

Explanation

To find the work done by the net force during the displacement from \( x = 0 \) to \( x = 2 \, \text{m} \) for a particle of mass \( 0.5 \, \text{kg} \) with velocity given by \( v = 5x^{5/2} \, \text{m/s} \), we can use the work-energy theorem, which states that the work done is equal to the change in kinetic energy of the particle.

### Step-by-Step Solution:

1. **Calculate the initial velocity at \( x = 0 \)**:
\[ v_1 = 5 \cdot 0^{5/2} = 0 \, \text{m/s} \]
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