A body of mass $m=2\text{ kg}$ is moving along the $x$-axis with a velocity of $v_i=4\text{ m/s}$. A force of $F=-6\text{ N}$ is applied for $t=2\text{ s}$. What is the final velocity $v_f$ of the body?

Solution

1. Identify the given values: mass $m=2\text{ kg}$, initial velocity $v_i=4\text{ m/s}$, force $F=-6\text{ N}$, and time $t=2\text{ s}$.
2. Apply the impulse-momentum theorem, which states that the impulse $F\cdot t$ equals the change in momentum $m(v_f-v_i)$.
3. Substitute the values into the equation: $(-6\text{ N})(2\text{ s})=(2\text{ kg})(v_f-4\text{ m/s})$.
4. Simplify the equation to $-12=2(v_f-4)$, which leads to $-6=v_f-4$.
5. Solve for the final velocity to get $v_f=-2\text{ m/s}$.
6. Hence the answer is (A).