Answer:
<em>Well, I think the best answer will be is </em><em>1.59 g/mL Good Luck!</em>
Answer: vl = 2.75 m/s vt = 1.5 m/s
Explanation:
If we assume that no external forces act during the collision, total momentum must be conserved.
If both cars are identical and also the drivers have the same mass, we can write the following:
m (vi1 + vi2) = m (vf1 + vf2) (1)
The sum of the initial speeds must be equal to the sum of the final ones.
If we are told that kinetic energy must be conserved also, simplifying, we can write:
vi1² + vi2² = vf1² + vf2² (2)
The only condition that satisfies (1) and (2) simultaneously is the one in which both masses exchange speeds, so we can write:
vf1 = vi2 and vf2 = vi1
If we call v1 to the speed of the leading car, and v2 to the trailing one, we can finally put the following:
vf1 = 2.75 m/s vf2 = 1.5 m/s
Speed is equal to distance traveled divided by the time. So it's 3.5 m/s
The rate of acceleration of the crate would be 1 m/s^2 because the equation for force is F=ma and when you plug in your numbers you get 10=10a so a=1
Answer:
(a) A = m/s^3, B = m/s.
(b) dx/dt = m/s.
Explanation:
(a)
![x = At^3 + Bt\\m = As^3 + Bs\\m = (\frac{m}{s^3})s^3 + (\frac{m}{s})s](https://tex.z-dn.net/?f=x%20%3D%20At%5E3%20%2B%20Bt%5C%5Cm%20%3D%20As%5E3%20%2B%20Bs%5C%5Cm%20%3D%20%28%5Cfrac%7Bm%7D%7Bs%5E3%7D%29s%5E3%20%2B%20%28%5Cfrac%7Bm%7D%7Bs%7D%29s)
Therefore, the dimension of A is m/s^3, and of B is m/s in order to satisfy the above equation.
(b) ![\frac{dx}{dt} = 3At^2 + B = 3(\frac{m}{s^3})s^2 + \frac{m}{s} = m/s](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%203At%5E2%20%2B%20B%20%3D%203%28%5Cfrac%7Bm%7D%7Bs%5E3%7D%29s%5E2%20%2B%20%5Cfrac%7Bm%7D%7Bs%7D%20%3D%20m%2Fs)
This makes sense, because the position function has a unit of 'm'. The derivative of the position function is velocity, and its unit is m/s.