Question

1. if you lengthen the time a change in velocity takes, will the force go up or down? use the equation;

\\\frac{\text{mass} \times \text{change in velocity}}{\text{time}}\\
to support your response. substitute reasonable numbers for mass, velocity and time to prove the effect.

Explanation:

State the relationship

$$ F = \frac{m \cdot \Delta v}{\Delta t} $$

Substitute numerical values

$$
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$$

Compare forces

$$ F_2 < F_1 \implies 5\text{ N} < 10\text{ N} $$

Answer:

The force will go down.

Using the equation:

$$ \text{Force} = \frac{\text{mass} \times \text{change in velocity}}{\text{time}} $$

If we let mass \(m = 10\text{ kg}\) and change in velocity \(\Delta v = 2\text{ m/s}\):

• With a short time \(\Delta t = 2\text{ s}\):

$$ F = \frac{10\text{ kg} \times 2\text{ m/s}}{2\text{ s}} = 10\text{ N} $$

• With a longer time \(\Delta t = 4\text{ s}\):

$$ F = \frac{10\text{ kg} \times 2\text{ m/s}}{4\text{ s}} = 5\text{ N} $$

Since \(5\text{ N} < 10\text{ N}\), lengthening the time decreases the force.