Question

a force of 5,500 n is applied to a 360 kg go-kart, initially sitting at rest. the final velocity of the go-kart is 140 m/s.

how long does the force act on the go-kart?

(t = ?\text{ s})

Explanation:

🆕 New Concept Discovered: Impulse-Momentum Theorem
Connecting force, time, and change in momentum

Step 1: Identify the given values

We are given the following values from the problem:

• Force, \( F = 5,500\text{ N} \)
• Mass, \( m = 360\text{ kg} \)
• Initial velocity, \( v_i = 0\text{ m/s} \) (since it is "initially sitting at rest")
• Final velocity, \( v_f = 140\text{ m/s} \)

Step 2: Use the Impulse-Momentum Theorem

The impulse-momentum theorem states that the impulse applied to an object is equal to its change in momentum.

Impulse is the force multiplied by the time interval over which it acts:

$$ \text{Impulse} = F \cdot t $$

Momentum (\( p \)) is mass multiplied by velocity. The change in momentum (\( \Delta p \)) is:

$$ \Delta p = m \cdot v_f - m \cdot v_i $$

Setting them equal to each other:

$$ F \cdot t = m(v_f - v_i) $$

Step 3: Solve for time (\( t \))

Substitute the known values into the equation:

$$ 5,500 \cdot t = 360 \cdot (140 - 0) $$

$$ 5,500 \cdot t = 360 \cdot 140 $$

$$ 5,500 \cdot t = 50,400 $$

Now, divide both sides by \( 5,500 \) to find \( t \):

$$ t = \frac{50,400}{5,500} $$

$$ t \approx 9.16\text{ s} $$

Rounding to the nearest tenth (or keeping it as a fraction if needed):

$$ t \approx 9.2\text{ s} $$

Answer:

\( 9.2 \) (or \( 9.16 \) if more decimal places are required)