Question

pre - and post - collision information is shown. identify the collision parameters that are consistent with the indicated change in momentum.
initial state
v = 4 m/s
4 kg
collision parameters
final state
v = 7 m/s
4 kg
tap an option below to select or change an answer.
(a + sign indicates a rightward direction, a - sign indicates a leftward direction.)
impulse = +12 n·s
f = +12 n, δt = 4 s
impulse = +11 n·s
δp = +3 kg·m/s
f = +3 n, δt = 3 s

Explanation:

Step1: Recall the impulse - momentum theorem

The impulse - momentum theorem states that $J=\Delta p$, where $J$ is the impulse and $\Delta p$ is the change in momentum. First, calculate the initial momentum $p_i$ and final momentum $p_f$ using the formula $p = mv$.
$p_i=mv_i$, with $m = 4\ kg$ and $v_i=4\ m/s$, so $p_i=4\times4=16\ kg\cdot m/s$.
$p_f=mv_f$, with $m = 4\ kg$ and $v_f = 7\ m/s$, so $p_f=4\times7 = 28\ kg\cdot m/s$.

Step2: Calculate the change in momentum

$\Delta p=p_f - p_i=28 - 16=12\ kg\cdot m/s$.
Since impulse $J=\Delta p$, the correct impulse value is $+ 12\ N\cdot s$ (the positive sign indicates the right - ward direction as per the problem's sign convention). Also, impulse $J = F\Delta t$. If $J = 12\ N\cdot s$ and $F = 12\ N$, then from $J=F\Delta t$, we have $\Delta t=\frac{J}{F}=\frac{12}{12}=1\ s$ (but we are mainly concerned with the impulse value here).

Answer:

Impulse $=+12\ N\cdot s$