Question

A train starting from rest first accelerates uniformly up to a speed of 80 km/h for time t, then it moves with a constant speed for time 3t. The average speed of the train for this duration of journey will be (in km/h) :

• A. 80
• B. 70
• C. 30
• D. 40

Answer 1

The Correct Option is B

The formula for average speed is:

\[ \text{Average speed} = \frac{\text{total distance}}{\text{time taken}} \]

For the initial acceleration phase:

\[ \text{Distance covered} = \frac{1}{2} \times \text{final speed} \times \text{time} = \frac{1}{2} \times 80 \times t = 40t \]

For the subsequent constant speed phase:

\[ \text{Distance covered} = \text{speed} \times \text{time} = 80 \times 3t = 240t \]

Total distance calculation:

\[ 40t + 240t = 280t \]

Total time calculation:

\[ t + 3t = 4t \]

Final average speed calculation:

\[ \text{Average speed} = \frac{280t}{4t} = 70 \, \text{km/h} \]