Question

If a body of mass \(2 \, \text{kg}\) moving with initial velocity of \(4 \, \text{m/s}\) is subjected to a force of \(3 \, \text{N}\) for a time of 2 seconds normal to the direction of its initial velocity, then the resultant velocity of the body is:

• A. 7 m s\(^{-1}\)
• B. 5 m s\(^{-1}\)
• C. 2 m s\(^{-1}\)
• D. 7.5 m s\(^{-1}\)

Hint:

When dealing with forces acting perpendicular to motion, use the work-energy theorem to find the change in kinetic energy and determine the final velocity.

Answer 1

The Correct Option is A

The force is acting perpendicular to the velocity, so we can use the work-energy principle. The work done on the body is equal to the change in kinetic energy: \[ W = F . d = \Delta KE. \] The displacement during the force is calculated using the equation: \[ d = \frac{1}{2} a t^2, \] where \(a = \frac{F}{m}\) is the acceleration. After finding the displacement, we can calculate the new velocity of the body using the kinetic energy equation: \[ KE_{\text{final}} = KE_{\text{initial}} + W. \] After calculation, the resultant velocity is: \[ 7 \, \text{m/s}. \]