In 0.25h it will move in 22.5 kilometers.
Momentum can be defined by the formula p=m*V (where m is mass and V is velocity) so if we plug in these numbers:
p = 2kg * 6m/s
p = 12 kgm/s
Answer:
Part A: ![t = v_0/a_0](https://tex.z-dn.net/?f=t%20%3D%20v_0%2Fa_0)
Part B: ![t = v_0/a_0](https://tex.z-dn.net/?f=t%20%3D%20v_0%2Fa_0)
Part C: ![v_0^2/a_0](https://tex.z-dn.net/?f=v_0%5E2%2Fa_0)
Explanation:
Part A:
We will use the following kinematics equation:
![v = v_0 + at\\0 = v_0 - a_0t\\t = \frac{v_0}{a_0}](https://tex.z-dn.net/?f=v%20%3D%20v_0%20%2B%20at%5C%5C0%20%3D%20v_0%20-%20a_0t%5C%5Ct%20%3D%20%5Cfrac%7Bv_0%7D%7Ba_0%7D)
Part B:
We will use the same kinematics equation:
![v = v_0 + at\\v_0 = 0 + a_0t\\t = \frac{v_0}{a_0}](https://tex.z-dn.net/?f=v%20%3D%20v_0%20%2B%20at%5C%5Cv_0%20%3D%200%20%2B%20a_0t%5C%5Ct%20%3D%20%5Cfrac%7Bv_0%7D%7Ba_0%7D)
Part C:
The total time takes is 2t.
So the train moves a distance of
![x = v_0(2t) = 2v_0(\frac{v_0}{a_0}) = \frac{2v_0^2}{a_0}](https://tex.z-dn.net/?f=x%20%3D%20v_0%282t%29%20%3D%202v_0%28%5Cfrac%7Bv_0%7D%7Ba_0%7D%29%20%3D%20%5Cfrac%7B2v_0%5E2%7D%7Ba_0%7D)
And the car moves a distance in Part A and in Part B:
![d_A = v_0t + \frac{1}{2}at^2 = v_0(\frac{v_0}{a_0}) - \frac{1}{2}a_0(\frac{v_0^2}{a_0^2}) = \frac{v_0^2}{a_0} - \frac{v_0^2}{2a_0} = \frac{v_0^2}{2a_0}\\d_B = v_0t + \frac{1}{2}at^2 = 0 + \frac{1}{2}a_0(\frac{v_0^2}{a_0^2}) = \frac{v_0^2}{2a_0}](https://tex.z-dn.net/?f=d_A%20%3D%20v_0t%20%2B%20%5Cfrac%7B1%7D%7B2%7Dat%5E2%20%3D%20v_0%28%5Cfrac%7Bv_0%7D%7Ba_0%7D%29%20-%20%5Cfrac%7B1%7D%7B2%7Da_0%28%5Cfrac%7Bv_0%5E2%7D%7Ba_0%5E2%7D%29%20%3D%20%5Cfrac%7Bv_0%5E2%7D%7Ba_0%7D%20-%20%5Cfrac%7Bv_0%5E2%7D%7B2a_0%7D%20%3D%20%5Cfrac%7Bv_0%5E2%7D%7B2a_0%7D%5C%5Cd_B%20%3D%20v_0t%20%2B%20%5Cfrac%7B1%7D%7B2%7Dat%5E2%20%3D%200%20%2B%20%5Cfrac%7B1%7D%7B2%7Da_0%28%5Cfrac%7Bv_0%5E2%7D%7Ba_0%5E2%7D%29%20%3D%20%5Cfrac%7Bv_0%5E2%7D%7B2a_0%7D)
So the total distance that the car traveled is ![d = \frac{v_0^2}{a_0}](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7Bv_0%5E2%7D%7Ba_0%7D)
The difference between the train and the car is
![x - d = \frac{2v_0^2}{a_0} - \frac{v_0^2}{a_0} = \frac{v_0^2}{a_0}](https://tex.z-dn.net/?f=x%20-%20d%20%3D%20%5Cfrac%7B2v_0%5E2%7D%7Ba_0%7D%20-%20%5Cfrac%7Bv_0%5E2%7D%7Ba_0%7D%20%3D%20%5Cfrac%7Bv_0%5E2%7D%7Ba_0%7D)
Answer:
Explanation:
Electric field at the surface of the the lead 208 = KQ/ R²
where K = 8.99 × 10⁹ Nm² /C²
Q ( total charge inside the nucleus) and e is the charge of a proton = Ne = 82 × 1.6 × 10⁻¹⁹ C = 1.312 × 10⁻¹⁷ C
V of the lead = 208 v of a proton assuming they both are sphere
4/3 πR³ =208( 4/3 πr³) where R is the radius of the sphere and r is the radius of the proton
R³ = 208 r³
R = ∛( 208 r³) = 5.92r
replace r with 1.20 x 10-15 m
R = 5.92 ×1.20 x 10-15 m = 7.11 × 10⁻¹⁵ m
E = ( 8.99 × 10⁹ Nm² /C² × 1.312 × 10⁻¹⁷ C ) / (7.11 × 10⁻¹⁵ m)² = 0.233 × 10²² N/C = 2.33 × 10²¹ N/C