While waiting in a car at a signal, an 80 kg man and his car are suddenly accelerated to a speed of `5 ms^(-1)` due to a rear-end collision by another vehicle. If the time of impact is 0.4s, the average force on the man is

Options

A. 100 N
B. 200 N
C. 500 N
D. 1000 N

Answer

To solve the problem, we need to calculate the average force exerted on the man during the collision. We can use the formula for force in terms of momentum:

\[ F = \frac{\Delta p}{\Delta t} \]

where:
- \( F \) is the average force,
- \( \Delta p \) is the change in momentum,
- \( \Delta t \) is the time of impact.

### Step 1: Calculate the change in momentum (\( \Delta p \))

The change in momentum can be calculated using the formula:

\[ \Delta p = m \cdot (v_f - v_i) \]

where:
- \( m \) is the mass of the man,
- \( v_f \) is the final velocity,
- \( v_i \) is the initial velocity.

Given:
- \( m = 80 \, \text{kg} \)
- \( v_f = 5 \, \text{m/s} \)
- \( v_i = 0 \, \text{m/s} \) (since the man was initially at rest)

Substituting the values:

\[ \Delta p = 80 \, \text{kg} \cdot (5 \, \text{m/s} - 0 \, \text{m/s}) \]
\[ \Delta p = 80 \, \text{kg} \cdot 5 \, \text{m/s} \]
\[ \Delta p = 400 \, \text{kg m/s} \]

### Step 2: Calculate the average force (\( F \))

Now, we can calculate the average force using the change in momentum and the time of impact:

\[ F = \frac{\Delta p}{\Delta t} \]

Given:
- \( \Delta t = 0.4 \, \text{s} \)

Substituting the values:

\[ F = \frac{400 \, \text{kg m/s}}{0.4 \, \text{s}} \]
\[ F = 1000 \, \text{N} \]

### Final Answer

The average force on the man is \( 1000 \, \text{N} \).

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