Question

A body of mass \(1\,\text{kg}\) moves along a straight line with a velocity \(v=2x^2\). The work done by the body during displacement from \(x=0\) to \(x=5\,\text{m}\) is _____ J.

• A. \(0\)
• B. \(250\)
• C. \(1250\)
• D. \(1000\)

Answer 1

The Correct Option is C

Concept: Work done equals change in kinetic energy: \[ W=\Delta K \] \[ K=\frac{1}{2}mv^2 \] Step 1: {Find velocity at the endpoints.} \[ v=2x^2 \] At \(x=0\): \[ v=0 \] At \(x=5\): \[ v=2(25)=50 \] Step 2: {Compute kinetic energies.} Initial kinetic energy: \[ K_i=0 \] Final kinetic energy: \[ K_f=\frac12(1)(50^2) \] \[ =1250 \] Step 3: {Find the work done.} \[ W=K_f-K_i \] \[ =1250-0 \] \[ =1250\ \text{J} \]