Question

1. if a force of 50 n is applied to an object for 0.2 s, and it changes its velocity by 10 m/s, what could be the mass of the object?

a. 1 kg
b. 2 kg

Explanation:

Step1: Recall Impulse-Momentum Theorem

Impulse \( J = F \times \Delta t \), and also \( J = m \times \Delta v \). So \( F \times \Delta t = m \times \Delta v \).

Step2: Plug in Values

Given \( F = 50\,\text{N} \), \( \Delta t = 0.2\,\text{s} \), \( \Delta v = 10\,\text{m/s} \). Rearrange formula for \( m \): \( m=\frac{F\times\Delta t}{\Delta v} \). Substitute values: \( m = \frac{50\times0.2}{10} \).

Step3: Calculate

\( 50\times0.2 = 10 \), then \( \frac{10}{10}=1\,\text{kg} \). Wait, but wait, maybe I made a mistake? Wait, no, let's check again. Wait, impulse is force times time, and change in momentum is mass times change in velocity. So \( F\Delta t = m\Delta v \). So \( m = \frac{F\Delta t}{\Delta v} = \frac{50*0.2}{10} = \frac{10}{10}=1\,\text{kg} \). But wait, the options are a. 1 kg, b. 2 kg. Wait, but maybe I messed up the formula? Wait, no, the impulse-momentum theorem is correct. So the mass should be 1 kg? Wait, but let me check again. 50 N times 0.2 s is 10 N·s. Change in velocity is 10 m/s. So mass is 10 / 10 = 1 kg. So the correct option is a. 1 kg? Wait, but maybe the problem has a typo? Or maybe I misread. Wait, the problem says "changes its velocity by 10 m/s". So yes, the calculation gives 1 kg. But wait, let me check the options again. Option a is 1 kg, option b is 2 kg. So according to the calculation, the answer is a. 1 kg. Wait, but maybe I made a mistake in the formula? Wait, no, impulse is force times time, momentum change is mass times velocity change. So the formula is correct. So the mass is 1 kg.

Answer:

a. 1 kg