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 find the average force on the man during the collision, we can use the formula for average force, which is derived from Newton's second law of motion:

\[ F_{\text{avg}} = \frac{\Delta p}{\Delta t} \]

where \( \Delta p \) is the change in momentum and \( \Delta t \) is the change in time.

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

The change in momentum can be calculated using the formula:

\[ \Delta p = m \cdot \Delta v \]

where:
- \( m \) is the mass of the man (80 kg),
- \( \Delta v \) is the change in velocity.

Since the man was initially at rest (0 m/s) and then accelerated to 5 m/s, we have:

\[ \Delta v = v_f - v_i = 5 \, \text{m/s} - 0 \, \text{m/s} = 5 \, \text{m/s} \]

Now substituting the values:

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

### Step 2: Calculate the average force (\( F_{\text{avg}} \))

Now that we have the change in momentum, we can calculate the average force. We know that the time of impact (\( \Delta t \)) is given as 0.4 seconds.

Using the formula for average force:

\[ F_{\text{avg}} = \frac{\Delta p}{\Delta t} = \frac{400 \, \text{kg m/s}}{0.4 \, \text{s}} \]

Calculating this gives:

\[ F_{\text{avg}} = 1000 \, \text{N} \]

### Final Answer

The average force on the man is **1000 N**.

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