Question

A bus travels with a speed of 40 km/hr in the 1st hour and 80 km/hr in the 2nd. What is the total distance covered by the bus in the two hours?
A. 40 km
B. 120 km
C. 80 km
D. 160 km

Answer 1

Hint: This question is based on linear motion of the body under a constant velocity. We can break the journey of the bus in two parts for constant velocities and find the distance covered. We can also use the average velocity formula to find the same.

Formula Used:
Total distance covered by the bus must be:
$d_{total} = v_{avg} \times t_{total} $

Complete step-by-step answer:
We are given that the velocity of the bus in the first hour of its journey is 40 km/hr, which in the second hour of the journey is 80 km/hr.
Therefore, the bus travels with an average velocity of:
$v_{avg} = \dfrac{40 + 80}{2} = \dfrac{120}{2}$ = 60 km/hr.

The total time of the journey is 2 hrs.
Therefore, the total distance is given as:
$d_{total} = 60 km/hr \times 2 hr$ = 120 km.

Therefore, the correct answer is option (B).

Additional information:
Here we assumed that the motion consisted of two separate constant velocities. This is usually not the case in real life. In real life, for the bus to attain a velocity of 80 km/hr, it has to undergo certain acceleration somewhere in the middle. To solve problems involving linear accelerated motion, we can always resort to equations of motion or differential equations (w.r.t. time).

Note: In this question a simple calculation that the bus is traveling 40 km in 1 hour means that in the first hour it must travel 40 km and in the second hour, it must travel 80 km giving the total distance of 120 km will work too. This method is too simple and time saving, so should be preferred here. But sometimes, the questions are not this simple, so the average velocity formula should be applied in that case.