Problem 67 - A Complete Resource Book in Physics for JEE Main

Question

The driver of three-wheeler moving with a speed of \(36 \mathrm{~km} / \mathrm{h}\) sees a child standing in the middle of the road and brings his vehicle to rest in \(4.0 \mathrm{~s}\) just in time to save the child. What is the average retarding force on the vehicle? The mass of the three-wheeler is \(400 \mathrm{~kg}\) and the mass of the driver is \(65 \mathrm{~kg}\). (A) \(1162.5 \mathrm{~N}\) (B) \(116.25 \mathrm{~N}\) (C) \(1112 \mathrm{~N}\) (D) None of these

Step-by-Step Solution

Answer

The short answer to the problem is: (A) \(1162.5 \mathrm{~N}\)

Step 1: Calculate the total mass of the system

First, we need to find the total mass of the system. Since we have the mass of the vehicle (m₁) and the mass of the driver (m₂), we can find the total mass (M) by adding the two masses. Total mass M = m₁ + m₂

Step 2: Convert the initial speed to m/s

The given speed is in km/h, and we need to convert it to meters per second (m/s) so that we can easily deal with units in our calculations. To convert from km/h to m/s, we need to multiply the given speed by (1000 m / 1 km) and divide by (3600 s / 1 h). \(v_0 = 36 \frac{km}{h} \cdot \frac{1000\,m}{1\,km} \cdot \frac{1\,h}{3600\,s}\)

Step 3: Find the final velocity

Since the vehicle comes to rest, the final velocity (v) of the vehicle will be 0 m/s. v = 0 m/s

Step 4: Calculate the average acceleration

Now, we will calculate the average acceleration (a) of the vehicle using the formula: \(a = \frac{v - v_0}{t}\) We have the values v, v₀, and t, so we can find the acceleration.

Step 5: Calculate the average retarding force

Finally, we will find the average retarding force (F) using the formula: F = M * a We have the value of M and a, so we can calculate the value of F. Once we solve the above steps, we will get the answer to the problem, which we can then match with the given options (A, B, C, or D).