Question

pre - and post - collision information is shown. identify the collision parameters that are consistent with the indicated change in momentum.
initial state
v = 5 m/s
2 kg
collision parameters
final state
v = 15 m/s
2 kg
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δp = +20 kg·m/s
impulse = +10 kg·m/s
impulse = +30 kg·m/s
f = +10 n, δt = 1 s
δp = +40 kg·m/s
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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.

Step2: Calculate initial momentum

The initial momentum $p_i = mv_i$, with $m = 2\ kg$ and $v_i=5\ m/s$. So $p_i=2\times5 = 10\ kg\cdot m/s$.

Step3: Calculate final momentum

The final momentum $p_f=mv_f$, with $m = 2\ kg$ and $v_f = 15\ m/s$. So $p_f=2\times15=30\ kg\cdot m/s$.

Step4: Calculate change in momentum

$\Delta p=p_f - p_i=30 - 10=20\ kg\cdot m/s$. According to the impulse - momentum theorem, the impulse $J=\Delta p = 20\ kg\cdot m/s$. Also, impulse $J = F\Delta t$. Given $F = 10\ N$ and $\Delta t=1\ s$, $J = 10\times1=10\ N\cdot s=10\ kg\cdot m/s$ is incorrect, and the correct change in momentum $\Delta p$ and impulse $J$ should be $20\ kg\cdot m/s$.

Answer:

$\Delta p=+20\ kg\cdot m/s$