Question

kristina has three skateboards for her skateboarding competitions. the brown and pink skateboards are of equal mass and more massive than the green skateboard, which has the least mass. one day, she tested the skateboards by giving each a push, but not from the same direction. use the information in the diagram to answer.
which skateboard(s) experienced the strongest force from kristinas push? how do you know?
before
brown skateboard: 2.2 kg (more mass) speed: 10 m/s
pink skateboard: 2.2 kg (more mass) speed: 7 m/s
green skateboard: 1.6 kg (less mass) speed 3 m/s
after
brown skateboard: speed 3 m/s (slowed down by 7 m/s)
pink skateboard: speed 14 m/s (speed up by 7 m/s)
green skateboard: speed 10 m/s (speed up by 7 m/s)
the pink skateboard experienced the strongest force for two reasons. it is a more massive object and it has the fastest ending speed.
the brown skateboard experienced the strongest force because it requires more force to slow an object down than to speed it up.
the brown and pink skateboards experienced the strongest force because they are both more massive than the green skateboard and they changed speed by the same amount.
all three skateboards experienced the same strength force because they changed speed by the same amount.

Explanation:

Step1: Recall Newton's second law

Force $F = ma$, where $m$ is mass and $a$ is acceleration. Acceleration $a=\frac{\Delta v}{\Delta t}$. Here we assume the time - interval $\Delta t$ of the push is the same for all skateboards.

Step2: Calculate acceleration for each skateboard

• Brown skateboard: Initial speed $v_1 = 10\ m/s$, final speed $v_2=3\ m/s$, $\Delta v=3 - 10=- 7\ m/s$.
• Pink skateboard: Initial speed $v_1 = 7\ m/s$, final speed $v_2 = 14\ m/s$, $\Delta v=14 - 7 = 7\ m/s$.
• Green skateboard: Initial speed $v_1 = 3\ m/s$, final speed $v_2 = 10\ m/s$, $\Delta v=10 - 3 = 7\ m/s$.

Step3: Analyze force based on mass and acceleration

The brown and pink skateboards have a mass of $m = 2.2\ kg$, and the green skateboard has a mass of $m = 1.6\ kg$. Since $F = ma$ and $\Delta t$ is assumed the same (so $a\propto\Delta v$), the brown and pink skateboards have a larger mass than the green skateboard and they have the same magnitude of speed - change ($|\Delta v|$) as the green skateboard. Larger mass with the same $|\Delta v|$ (and thus same magnitude of acceleration in terms of calculation) means a larger force.

Answer:

The brown and pink skateboards experienced the strongest force because they are both more massive than the green skateboard and they changed speed by the same amount.