Question:
A body travelling along a straight line traverse one-third the distance with a velocity of $ 5 \,m/s $ . The remaining part of the distance was covered with velocity $ 3 \,m/s $ for half the time and with velocity $ 2 \,m/s $ for the other half of the time. The average velocity of the body over the whole time of motion will be
A body travelling along a straight line traverse one-third the distance with a velocity of $ 5 \,m/s $ . The remaining part of the distance was covered with velocity $ 3 \,m/s $ for half the time and with velocity $ 2 \,m/s $ for the other half of the time. The average velocity of the body over the whole time of motion will be
Updated On: Jun 14, 2022
- $ 3\, m/s $
- $ 5\, m/s $
- $ 2\, m/s $
- $ 2.5\, m/s $
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The Correct Option is B
Solution and Explanation
Time taken in the one third part of total distance coverd is $t_1$ and for remaining part is $2t_2$
$t_1 = \frac{x/3}{5} = \frac{x}{15}$
$ x_1 + x_2 = \frac{2}{3} x$
$ 3t_2 + 2t_2 = \frac{2}{3} x$
$5t_2 = \frac{2}{3}x$
$t_2 = \frac{2x}{15}$
Total time $ = t_1 + 2t_2$
$ = \frac{x}{15} + \frac{2x}{15}$
$t = \frac{3x}{15} = \frac{x}{5}$
Average velocity
$v = \frac{x}{\frac{x}{5}}$
$ v = 5\,m/s$
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.