Question

A train starts from rest and moves with a constant acceleration of 2.0 m/s² for half a minute. The brakes are then applied and the train comes to rest in one minute. Find the total distance moved by the train.

Answer 1

Initial velocity, u = 0
Acceleration, a = 2 m/s²
Let the final velocity be v before the brakes are applied.
Now,           
t = 30 s
v = u + at
v = 0 + 2 × 30
 ⇒ v = 60 m/s

\[s_1 = ut + \frac{1}{2}a t^2\]

\[\Rightarrow s_1 = \frac{1}{2} \times 2 \times \left( 30 \right)^2 = 900 \text{ m } \]

When the brakes are applied:
u' = 60 m/s
v' = 0
t = 1 min = 60 s
Acceleration:

\[a' = \frac{\left( v - u \right)}{t} = \frac{\left( 0 - 60 \right)}{60} = - 1 \text{ m } / s^2 \]
\[ s_2 = \frac{v^2 - u^2}{2a'} = \frac{0^2 - {60}^2}{2\left( - 1 \right)} = 1800 \text{ m } \]

s = s₁ + s₂ = 1800 + 900 = 2700 m
⇒ s = 2.7 km