A vehicle of mass 120kg is moving with a velocity of 90kmph What force should be applied on the vehicle to stop it in 5s.

Answer

To solve the problem, we need to determine the force required to stop a vehicle of mass 120 kg moving at a velocity of 90 km/h in 5 seconds. Here are the steps to find the solution:

### Step 1: Convert the velocity from km/h to m/s
The initial velocity \( u \) is given as 90 km/h. We need to convert this to meters per second (m/s) using the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]
Thus,
\[ u = 90 \times \frac{5}{18} = 25 \text{ m/s} \]

### Step 2: Identify the final velocity
Since the vehicle is to be stopped, the final velocity \( v \) will be:
\[ v = 0 \text{ m/s} \]

### Step 3: Use the first equation of motion to find acceleration
We can use the first equation of motion:
\[ v = u + at \]
Where:
- \( v \) is the final velocity (0 m/s)
- \( u \) is the initial velocity (25 m/s)
- \( a \) is the acceleration
- \( t \) is the time (5 s)

Substituting the known values:
\[ 0 = 25 + a \times 5 \]
Rearranging gives:
\[ a \times 5 = -25 \implies a = -\frac{25}{5} = -5 \text{ m/s}^2 \]
The negative sign indicates that this is a deceleration.

### Step 4: Calculate the force using Newton's second law
According to Newton's second law:
\[ F = ma \]
Where:
- \( F \) is the force
- \( m \) is the mass (120 kg)
- \( a \) is the acceleration (-5 m/s²)

Substituting the values:
\[ F = 120 \times (-5) = -600 \text{ N} \]
The negative sign indicates that the force is applied in the opposite direction of motion.

### Step 5: Present the final answer
The magnitude of the force required to stop the vehicle is:
\[ F = 600 \text{ N} \]

### Summary of the solution
To stop a vehicle of mass 120 kg moving at 90 km/h in 5 seconds, a force of 600 N must be applied in the opposite direction of the vehicle's motion.

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