A scooter of mass 150 kg is moving with a uniform velocity of 108 km/h. Then the force required to stop he vehicle in 10s is

Options

A. 360 N
B. 420 N
C. 450 N
D. None of these

Explanation

To solve the problem of determining the force required to stop a scooter of mass 150 kg moving at a uniform velocity of 108 km/h in 10 seconds, we can follow these steps:

### Step 1: Convert the velocity from km/h to m/s
The given velocity is 108 km/h. To convert this to meters per second (m/s), we use the conversion factor:
\[ \text{Velocity (m/s)} = \text{Velocity (km/h)} \times \frac{5}{18} \]
Calculating:
\[ \text{Velocity} = 108 \times \frac{5}{18} = 30 \text{ m/s} \]

### Step 2: Identify the initial and final velocities
- Initial velocity \( u = 30 \, \text{m/s} \)
- Final velocity \( v = 0 \, \text{m/s} \) (since the scooter comes to a stop)

### Step 3: Determine the time taken to stop
The time taken to stop is given as \( t = 10 \, \text{s} \).

### Step 4: Use the first equation of motion to find acceleration
Using the first equation of motion:
\[ v = u + at \]
Substituting the known values:
\[ 0 = 30 + a \times 10 \]
Rearranging to find acceleration \( a \):
\[ a = \frac{-30}{10} = -3 \, \text{m/s}^2 \]
The negative sign indicates that the acceleration is in the opposite direction of the motion.

### Step 5: Calculate the force using Newton's second law
Using Newton's second law:
\[ F = m \cdot a \]
Where:
- \( m = 150 \, \text{kg} \)
- \( a = -3 \, \text{m/s}^2 \)

Calculating the force:
\[ F = 150 \cdot (-3) = -450 \, \text{N} \]
The negative sign indicates that the force is applied in the opposite direction of the scooter's motion.

### Step 6: State the final answer
The force required to stop the scooter in 10 seconds is:
\[ \text{Force} = 450 \, \text{N} \]

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