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) : 

(1) 80 

(2) 70 

(3) 30 

(4) 40

Answer 1

Correct option is :  (2) 70

\(\text { average speed }=\frac{\text { distance }}{\text { time }}\)

\(=\frac{\frac{1}{2}(\mathrm{t})(80)+80 \times 3 \mathrm{t}}{4 \mathrm{t}}\)

\(=\frac{40 \mathrm{t}+240 \mathrm{t}}{4 \mathrm{t}} \)

\(=\frac{280}{4}=70 \mathrm{~km} / \mathrm{hr}\)