Question

A freight train has a mass of 3.8 x 10^7 kg. The locomotive can exert a force of 6.5 x 10^5 N to pull the train.

Required:
a. How long does it take the train to go from rest to 50 km/hr?
b. If there is air resistance of 2.0 x 10^5 N, what is the acceleration of the train, and how long does it take the train to go from rest to 50 km/hr?

Answer 1

(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

Step-by-step 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 = (m(v-u))/(t)\\\\t = (m(v-u))/(F)\\\\t = (3.8*10^7(13.889-0))/(6.5*10^5)\\\\t = 811.97 \ s`

(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 = (4.5 * 10^5 )/(m)\\\\a = (4.5 * 10^5 )/(3.8*10^7)\\\\a = 0.012 \ m/s^2`

(ii) time taken for the plane to reach 50 km/hr is given by;

`F = (m(v-u))/(t)\\\\t = (m(v-u))/(F)\\\\t = (3.8*10^7(13.889-0))/(4.5*10^5)\\\\t = 1172.85 \ s`