Question

A body of mass \(2\) kg changes its velocity from \((3\hat i-4\hat j)\,m/s\) to \((6\hat j+2\hat k)\,m/s\). What is the change in kinetic energy of the body?

• A. \(15\,J\)
• B. \(12\,J\)
• C. \(18\,J\)
• D. \(20\,J\)

Hint:

For vector velocity, first calculate \(v^2\) by squaring and adding components.

Answer 1

The Correct Option is A

Concept:
Kinetic energy of a body is: \[ K=\frac{1}{2}mv^2 \] where \(v^2\) is the square of the magnitude of velocity.

Step 1: Initial velocity: \[ \vec v_i=3\hat i-4\hat j \] \[ v_i^2=3^2+(-4)^2=9+16=25 \]

Step 2: Final velocity: \[ \vec v_f=6\hat j+2\hat k \] \[ v_f^2=6^2+2^2=36+4=40 \]

Step 3: Change in kinetic energy: \[ \Delta K=\frac{1}{2}m(v_f^2-v_i^2) \]

Step 4: Given \(m=2\,kg\): \[ \Delta K=\frac{1}{2}(2)(40-25) \] \[ \Delta K=15\,J \] \[ \boxed{15\,J} \]