Answer:
20 kg
Explanation:
Mass equals force divided by acceleration, so divide 100 N by 5 m/s2 and you get your mass: 20 kg
Answer:
A) ![\frac{g}{b}(1-e^{-bt})](https://tex.z-dn.net/?f=%5Cfrac%7Bg%7D%7Bb%7D%281-e%5E%7B-bt%7D%29)
Explanation:
Since a = g - bv,
We can substitute a = dv/dt into the equation.
Then, the equation will be like dv/dt = g - bv.
So we got first order differential equation.
As known, v = 0 at t = 0, and v = g/b at t = ∞.
Since
⇒ ![\frac{dv}{ \frac{g}{b} - v}= bdt](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7B%20%5Cfrac%7Bg%7D%7Bb%7D%20-%20v%7D%3D%20bdt)
So take the integral of both side.
![- ln (\frac{g}{b} - v) = bt + C](https://tex.z-dn.net/?f=-%20ln%20%28%5Cfrac%7Bg%7D%7Bb%7D%20-%20v%29%20%3D%20bt%20%2B%20C)
Since for t=0, v = 0 ⇒ ![C =- ln (\frac{g}{b})](https://tex.z-dn.net/?f=C%20%3D-%20ln%20%28%5Cfrac%7Bg%7D%7Bb%7D%29)
![v = \frac{g}{b} + e^{-bt-ln(\frac{g}{b})} = \frac{g}{b}- \frac{g}{b}e^{-bt} = \frac{g}{b}(1-e^{-bt})](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bg%7D%7Bb%7D%20%2B%20e%5E%7B-bt-ln%28%5Cfrac%7Bg%7D%7Bb%7D%29%7D%20%3D%20%5Cfrac%7Bg%7D%7Bb%7D-%20%5Cfrac%7Bg%7D%7Bb%7De%5E%7B-bt%7D%20%3D%20%5Cfrac%7Bg%7D%7Bb%7D%281-e%5E%7B-bt%7D%29)
Answer:
-2200 N
Explanation:
The change in momentum of Sarah is equal to the impulse, which is the product between the force exerted by the seatbelt on Sarah and the time during which the force is applied:
where
m is the mass
is the change in velocity
F is the average force
is the duration of the collision
In this problem:, we have:
m = 55 kg is Sarah's mass
is the change in velocity
is the duration of the collision
Solving for F, we find the force exerted by the seatbelt on Sarah:
Where the negative sign indicates that the direction of the force is opposite to that of Sarah's initial velocity.