Question

The force to be applied to a body of mass $200\ \text{g}$ to change its velocity by $25\ \text{m s}^{-1}$ in $5\ \text{s}$ is:

• A. 2.5 N
• B. 50 N
• C. 3 N
• D. 30 N
• E. 1 N

Hint:

Always convert mass to kilograms (SI unit) before calculating force in Newtons.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This problem applies Newton's second law of motion, which relates force, mass, and acceleration. Force is the rate of change of linear momentum.
Step 2: Key Formula or Approach:
1. Newton's second law can be written as \( F = ma \). 2. Acceleration (a) is the rate of change of velocity: \( a = \frac{\Delta v}{\Delta t} \), where \( \Delta v \) is the change in velocity and \( \Delta t \) is the time interval. 3. Combining these, we get \( F = m \frac{\Delta v}{\Delta t} \). 4. Ensure all units are in the SI system (mass in kg, velocity in m/s, time in s, force in N). Step 3: Detailed Explanation:
We are given: - Mass, \( m = 200 \text{ g} \) - Change in velocity, \( \Delta v = 25 \text{ m/s} \) - Time interval, \( \Delta t = 5 \text{ s} \) First, convert the mass to SI units (kilograms): \[ m = 200 \text{ g} = \frac{200}{1000} \text{ kg} = 0.2 \text{ kg} \] Now, calculate the acceleration: \[ a = \frac{\Delta v}{\Delta t} = \frac{25 \text{ m/s}}{5 \text{ s}} = 5 \text{ m/s}^2 \] Finally, calculate the force using \( F = ma \): \[ F = (0.2 \text{ kg}) \times (5 \text{ m/s}^2) = 1.0 \text{ N} \] Step 4: Final Answer:
The force to be applied is 1 N.