Question

A train starting from rest attains a velocity of 72 km/h in 5 minutes. Assuming that the acceleration is uniform. The distance travelled by train for the above velocity is

• A. 3 km
• B. 5 km
• C. 8 km
• D. 12 km

Hint:

Using \(s = \frac{u + v}{2} \times t\) is often much faster than calculating acceleration first, especially when you don't need the acceleration value for anything else. Keep an eye on unit consistency (hours vs minutes).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
A train starts from rest (initial velocity = 0) and reaches a certain final velocity in a given time with uniform acceleration. We need to find the distance covered during this time.


Step 2: Key Formula or Approach:
For uniform acceleration, the distance \(s\) can be calculated using the average velocity: \[ \text{Average Velocity} = \frac{u + v}{2} \] \[ s = \text{Average Velocity} \times t = \left( \frac{u + v}{2} \right) \times t \] Alternatively, find acceleration \(a = (v-u)/t\) and use \(s = ut + \frac{1}{2}at^2\).


Step 3: Detailed Explanation:
Initial velocity, \(u = 0\)
Final velocity, \(v = 72 \text{ km/h}\)
Time, \(t = 5 \text{ minutes}\). We must convert this to hours to match the units of velocity. \[ t = \frac{5}{60} \text{ hours} = \frac{1}{12} \text{ hours} \] Using the average velocity formula for distance: \[ s = \left( \frac{0 + 72}{2} \right) \times \frac{1}{12} \] \[ s = 36 \times \frac{1}{12} \] \[ s = 3 \text{ km} \]

Step 4: Final Answer:
The distance travelled by the train is 3 km.