A constant force of 5N acts for 5 seconds on a mass of 5kg initially at rest. Calculate the final momentum

1. Analyze the question

We are given:

• Force ($F$) = $5\text{ N}$
• Time ($t$) = $5\text{ s}$
• Mass ($m$) = $5\text{ kg}$
• Initial velocity ($u$) = $0\text{ m/s}$ (since it is initially at rest)
• We need to find the final momentum ($p$).

2. Explain the concept

Momentum ($p$) is defined as the product of mass and velocity ($p = mv$). According to Newton's Second Law of Motion, the rate of change of momentum is equal to the applied force. This is expressed by the Impulse-Momentum Theorem:

Since the object starts from rest ($u = 0$), the final momentum is simply equal to the impulse applied to the object.

3. Show the solution

Step 1: Identify the formula for Impulse.

Step 2: Calculate the Impulse.

Step 3: Relate Impulse to Momentum. Since Impulse = Change in Momentum ($\Delta p$):

Because the object starts from rest, $p_{\text{initial}} = m \times 0 = 0$. Therefore:

(Note: The unit of Impulse, Newton-seconds (Ns), is equivalent to the unit of momentum, $\text{kgms}^{-1}$.)

4. Identify the answer

Comparing our result to the options provided: A. $125\text{ kgms}^{-1}$ B. $25\text{ kgms}^{-1}$ C. $15\text{ kgms}^{-1}$ D. $0\text{ kgms}^{-1}$

The correct option is B.

5. Tip

Whenever you see a question involving "Force," "Time," and "Momentum," think of the word Impulse. Remember the acronym FIT: Force $\times$ Impulse = Time (or more accurately, $F \times t = \Delta p$). This saves you the stress of calculating acceleration and final velocity separately!