A car of mass 2400 kg moving with a velocity of 20 m `s^(-1)` is stopped in 10 seconds on applying brakes Calculate the retardation and the retarding force.

Answer

To solve the problem of a car of mass 2400 kg moving with a velocity of 20 m/s that stops in 10 seconds, we need to calculate the retardation and the retarding force. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Mass of the car (m) = 2400 kg
- Initial velocity (u) = 20 m/s
- Final velocity (v) = 0 m/s (since the car stops)
- Time taken to stop (t) = 10 seconds

### Step 2: Calculate the retardation
Retardation (a) can be calculated using the formula for acceleration:
\[ a = \frac{v - u}{t} \]
Substituting the known values:
\[ a = \frac{0 - 20}{10} = \frac{-20}{10} = -2 \, \text{m/s}^2 \]
Thus, the retardation is \( -2 \, \text{m/s}^2 \).

### Step 3: Calculate the retarding force
The retarding force (F) can be calculated using Newton's second law of motion:
\[ F = m \cdot a \]
Substituting the values we have:
\[ F = 2400 \, \text{kg} \cdot (-2 \, \text{m/s}^2) = -4800 \, \text{N} \]
Thus, the retarding force is \( -4800 \, \text{N} \).

### Final Answers:
- Retardation: \( -2 \, \text{m/s}^2 \)
- Retarding Force: \( -4800 \, \text{N} \)

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