Answer:
(a) The time taken for the plane to reach 50 km/hr is 811.97 s
(b) (i) the acceleration of the plane is 0.012 m/s²
(ii) The time taken for the plane to reach 50 km/hr is 1172.85 s
Explanation:
Given;
mass of the freight train, m = 3.8 x 10⁷ kg
force applied to pull the train, F = 6.5 x 10⁵ N
a. How long does it take the train to go from rest to 50 km/hr?
Given;
initial velocity, u = 0
final velocity, v = 50 km/hr = 13.889 m/s
Apply Newton's second law of motion to determine the time traveled by the train at the given speed;
![F = ma = \frac{m(v-u)}{t}\\\\t = \frac{m(v-u)}{F}\\\\t = \frac{3.8*10^7(13.889-0)}{6.5*10^5}\\\\t = 811.97 \ s](https://tex.z-dn.net/?f=F%20%3D%20ma%20%3D%20%5Cfrac%7Bm%28v-u%29%7D%7Bt%7D%5C%5C%5C%5Ct%20%3D%20%20%5Cfrac%7Bm%28v-u%29%7D%7BF%7D%5C%5C%5C%5Ct%20%3D%20%20%5Cfrac%7B3.8%2A10%5E7%2813.889-0%29%7D%7B6.5%2A10%5E5%7D%5C%5C%5C%5Ct%20%3D%20811.97%20%5C%20s)
(b)
(i) the acceleration of the plane
Given;
air resistance, = 2.0 x 10⁵ N
Apply Newton's second law of motion;
∑F = ma
6.5 x 10⁵ N - 2.0 x 10⁵ N = ma
4.5 x 10⁵ N = ma
![a = \frac{4.5 * 10^5 }{m}\\\\a = \frac{4.5 * 10^5 }{3.8*10^7}\\\\a = 0.012 \ m/s^2](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B4.5%20%2A%2010%5E5%20%7D%7Bm%7D%5C%5C%5C%5Ca%20%3D%20%20%20%5Cfrac%7B4.5%20%2A%2010%5E5%20%7D%7B3.8%2A10%5E7%7D%5C%5C%5C%5Ca%20%3D%200.012%20%5C%20m%2Fs%5E2)
(ii) time taken for the plane to reach 50 km/hr is given by;
![F = \frac{m(v-u)}{t}\\\\t = \frac{m(v-u)}{F}\\\\t = \frac{3.8*10^7(13.889-0)}{4.5*10^5}\\\\t = 1172.85 \ s](https://tex.z-dn.net/?f=F%20%3D%20%20%5Cfrac%7Bm%28v-u%29%7D%7Bt%7D%5C%5C%5C%5Ct%20%3D%20%20%5Cfrac%7Bm%28v-u%29%7D%7BF%7D%5C%5C%5C%5Ct%20%3D%20%20%5Cfrac%7B3.8%2A10%5E7%2813.889-0%29%7D%7B4.5%2A10%5E5%7D%5C%5C%5C%5Ct%20%3D%201172.85%20%5C%20s)