A truck of mass `2xx10^3kg` travelling at `4m//s` is brought to rest in `2s` when it strikes a wall. What force (assume constant) is exerted by the wall?

Explanation

To solve the problem, we need to determine the force exerted by the wall on the truck when it comes to rest. We can use the concept of impulse and momentum to find the solution.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the truck, \( m = 2 \times 10^3 \, \text{kg} \)
- Initial velocity of the truck, \( v_i = 4 \, \text{m/s} \)
- Final velocity of the truck, \( v_f = 0 \, \text{m/s} \) (since it comes to rest)
- Time taken to come to rest, \( t = 2 \, \text{s} \)

2. **Calculate the Change in Momentum:**
The change in momentum (\( \Delta p \)) is given by:
\[ \Delta p = m(v_f - v_i) \]
Substituting the values:
\[ \Delta p = 2 \times 10^3 \, \text{kg} \times (0 - 4 \, \text{m/s}) = 2 \times 10^3 \, \text{kg} \times (-4 \, \text{m/s}) = -8 \times 10^3 \, \text{kg m/s} \]

3. **Use the Impulse-Momentum Theorem:**
According to the impulse-momentum theorem:
\[ \text{Impulse} = \Delta p = F \cdot t \]
Rearranging for force (\( F \)):
\[ F = \frac{\Delta p}{t} \]
Substituting the values:
\[ F = \frac{-8 \times 10^3 \, \text{kg m/s}}{2 \, \text{s}} = -4 \times 10^3 \, \text{N} \]

4. **Interpret the Result:**
The negative sign indicates that the force exerted by the wall is in the opposite direction to the truck's initial motion. Thus, the magnitude of the force exerted by the wall is:
\[ F = 4 \times 10^3 \, \text{N} \]

### Final Answer:
The force exerted by the wall is \( 4 \times 10^3 \, \text{N} \).

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