Question

The force acting on the particle of 0.2 kg mass whose displacement is described by the equation \( x = 3t + 7t^2 \, \text{m} \)

• A. 1.0 N
• B. 3.2 N
• C. 6.4 N
• D. 8.6 N
• E. 2.8 N

Hint:

For constant acceleration, calculate the force by multiplying mass with constant acceleration.

Answer 1

Answer: (E)

To find the force acting on the particle, we need to use Newton’s second law of motion, \( F = ma \), where \( a \) is the acceleration of the particle. 1. First, we differentiate the displacement equation to get the velocity: \[ x(t) = 3t + 7t^2 \] \[ v(t) = \frac{dx}{dt} = 3 + 14t \] 2. Then, we differentiate the velocity equation to get the acceleration: \[ a(t) = \frac{dv}{dt} = 14 \] The acceleration is constant, \( a(t) = 14 \, \text{m/s}^2 \). 3. Using Newton's second law: \[ F = ma = 0.2 \, \text{kg} \times 14 \, \text{m/s}^2 = 2.8 \, \text{N} \] Thus, the correct answer is (E) 2.8 N.