Question

A vehicle moving at 36 km/hr is to be stopped by applying brakes in the next 5 m. If the vehicle weighs 2000 kg, determine the average force that must be applied on it.

• A. \( 10^4 \, \text{N} \)
• B. \( 2 \times 10^4 \, \text{N} \)
• C. \( 3 \times 10^4 \, \text{N} \)
• D. \( 5 \times 10^3 \, \text{N} \)
• E. \( 10^3 \, \text{N} \)

Hint:

To calculate the force required to stop a vehicle, use the equation of motion \( v^2 = u^2 + 2as \), where \( u \) is the initial velocity, \( a \) is the acceleration, and \( s \) is the stopping distance. Then apply \( F = ma \) to find the force.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The vehicle is brought to a complete halt, meaning its final velocity is zero.
We must calculate the deceleration required to stop it within the specified distance, and then apply Newton's second law.
Step 2: Key Formula or Approach:
Use the third equation of motion to find the acceleration: \( v^{2} = u^{2} + 2as \).
Then, determine the required force using Newton's second law: \( F = ma \).
Step 3: Detailed Explanation:
First, we must convert the initial velocity from km/hr to m/s:
\[ u = 36 \text{ km/hr} = 36 \times \frac{5}{18} \text{ m/s} = 10 \text{ m/s} \] The final velocity is \( v = 0 \text{ m/s} \).
The stopping distance is \( s = 5 \text{ m} \).
Using the kinematic equation:
\[ 0^{2} = (10)^{2} + 2(a)(5) \] \[ 0 = 100 + 10a \] \[ 10a = -100 \implies a = -10 \text{ m/s}^{2} \] The negative sign indicates that it is a retarding force.
Now, calculate the magnitude of the average force:
Mass, \( m = 2000 \text{ kg} \).
\[ F = |ma| = 2000 \times 10 = 20000 \text{ N} \] This can be written in scientific notation as \( 2 \times 10^{4} \text{ N} \).
Step 4: Final Answer:
The average stopping force required is \(2 \times 10^{4} \text{ N}\).