Question

A body of mass 5 kg is moving in a straight line. The relation between its displacement and time is \( x = (t^3 - 2t - 10) \) m. What is the force acting on it at the end of 5 seconds?

• A. 150 N
• B. 120 N
• C. 80 N
• D. 100 N

Hint:

Force is the product of mass and acceleration. First, find the velocity and acceleration by differentiating the displacement equation.

Answer 1

The Correct Option is A

Step 1: Finding velocity.
Velocity is the derivative of displacement with respect to time. The displacement is given by: \[ x = t^3 - 2t - 10 \] Taking the derivative with respect to time \( t \): \[ v = \frac{dx}{dt} = 3t^2 - 2 \] Step 2: Finding acceleration.
Acceleration is the derivative of velocity with respect to time. Taking the derivative of \( v \): \[ a = \frac{dv}{dt} = 6t \] Step 3: Finding force.
Force is given by \( F = ma \). Substituting the values for mass \( m = 5 \, \text{kg} \) and acceleration at \( t = 5 \): \[ a = 6 \times 5 = 30 \, \text{m/s}^2 \] Thus, the force is: \[ F = 5 \times 30 = 150 \, \text{N} \] Thus, the correct answer is (A) 150 N.