A car moves a distance of 200 m. It covers the first half of the distance at speed 40 km/h and the second half of distance at speed v. The average speed is 48 km/h. The value of v is
- 56 km/h
- 60 km/h
- 50 km/h
- 48 km/h
The Correct Option is B
Solution and Explanation
Total time taken $=\frac{100}{40}+\frac{100}{v}$
Average speed $=\frac{total\, distance\, travelled}{total\, time\, taken}$
$48=\frac{200}{\bigg(\frac{100}{40}+\frac{100}{v}\bigg)}$ or $48=\frac{2}{\bigg(\frac{1}{40}+\frac{1}{v}\bigg)}$
or $\, \, \frac{1}{40}+\frac{1}{v}=\frac{1}{24}$
or $\, \, \frac{1}{v}=\frac{1}{24}-\frac{1}{40}=\frac{5-3}{120}=\frac{1}{60}$
or $ \, \, v = 60\, km/hr$
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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.