Question

A car of mass 1500 kg is moving with 20 ms\(^{-1}\) velocity. If the breaks are applied it comes to rest in 5 seconds, then the retarding force is

• A. \( 9000 \, \text{N} \)
• B. \( 6000 \, \text{N} \)
• C. \( 12000 \, \text{N} \)
• D. \( 3000 \, \text{N} \)

Hint:

When calculating the retarding force, use the equation of motion to first determine the acceleration (or deceleration), and then apply Newton's second law to find the force.

Answer 1

The Correct Option is B

We are given that the car is moving with an initial velocity of \( 20 \, \text{m/s} \), the mass of the car is \( 1500 \, \text{kg} \), and the time taken to come to rest is \( 5 \, \text{seconds} \). The retardation force is calculated using the equation of motion: \[ F = ma \] Where \( a \) is the acceleration (deceleration in this case), which can be found using the formula: \[ a = \frac{\Delta v}{t} = \frac{0 - 20}{5} = -4 \, \text{m/s}^2 \] Now, applying Newton's second law: \[ F = ma = 1500 \times (-4) = -6000 \, \text{N} \] Thus, the retarding force is \( 6000 \, \text{N} \). Hence, the correct answer is option (2).

Answer 2

Step 1: Identify given values.
Mass \( m = 1500 \, \text{kg} \)
Initial velocity \( u = 20 \, \text{m/s} \)
Final velocity \( v = 0 \)
Time \( t = 5 \, \text{s} \)

Step 2: Use first equation of motion to find acceleration.
\[ v = u + at \Rightarrow 0 = 20 + a \times 5 \Rightarrow a = -4 \, \text{m/s}^2 \]

Step 3: Calculate the retarding force.
\[ F = ma = 1500 \times (-4) = -6000 \, \text{N} \]
(The negative sign indicates retardation.)

Final Answer: \( 6000 \, \text{N} \)