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 3 t. The average speed of the train for this duration of journey will be (in km / h) :

Solution

Physics sir · 3 steps

Average speed is total distance over total time, so find the distance in each phase first.

1. Accelerating phase. The speed rises uniformly from 0 to 80 km/h, so the average speed in this phase is (0+80)/2 = 40 km/h. Distance covered is 40t.
2. Constant-speed phase. The train moves at 80 km/h for time 3t, so it covers 80 × 3t = 240t.

   v_(avg) = (40t + 240t)/(t + 3t) = 280t/4t = 70 km/h

3. So. The average speed for the whole journey is 70 km/h, option (a).

The idea to keep. Never average the speeds of different phases directly. Find each phase's distance (area under the v–t graph) and divide the total by the total time.

Answer from the NTA final answer key. Solution by PrepWiser.