Question

A body moves from A to B with a constant speed of 20 kmph and then from B to A with a constant speed of 30 kmph. Then the average speed of the car is ?

Answer 1

The answer is in image

Answer 2

Answer:

$v_{av}\ =\ 24\ km/h.$

Explanation:

• Speed of the body moving towards A to B = $v_1\ =\ 20 km/h$
• Speed of the body moving towards B to A = $v_2\ =\ 30\ km/h$

In case, the body moving towards A to B,

Let $t_1$ be the total time taken by the body. and s be the total distance traveled by the body from A to B.

$\therefore s\ =\ v_1t_1\Rightarrow t_1\ =\ \dfrac{s}{v_1}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,eqn (1)$

In case, the body moving towards B to A,

Let $t_2$ be the total time taken by the body. and s be the total distance traveled by the body from B to A.

$\therefore s\ =\ v_2t_2\\\Rightarrow t_2\ =\ \dfrac{s}{v_2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,eqn (2)$

Both the velocities are constant.

Therefore from the average velocity formula

$\therefore v_{av}\ =\ \dfrac{s_1\ +\ s_2}{t_1\ +\ t_2}\\\Rightarrow v_{av}\ =\ \dfrac{s\ +\ s}{\dfrac{s}{v_1}\ +\ \dfrac{s}{v_2}}\\\Rightarrow v_{av}\ =\ \dfrac{2s}{\dfrac{sv_2\ +\ sv_1}{v_1v_2}}\\\Rightarow v_{av}\ =\ \dfrac{2sv_1v_2}{s(v_1\ +\ v_2)}\\\Rightarrow v_{av}\ =\ \dfrac{2v_1v_2}{v_1\ +\ v_2}\\\Rightarrow v_{av}\ =\ \dfrac{2\times 20\times 30}{20\ +\ 30}\\\Rightarrow v_{av}\ =\ 24\ km/h.$

Hence the average speed of the body is 24 km/h.