Question:
A car moving on a straight road covers $ 1/3 $ of the distance with $ 25\,km/h $ and rest with $ 75\,km/h $ . The average speed is
A car moving on a straight road covers $ 1/3 $ of the distance with $ 25\,km/h $ and rest with $ 75\,km/h $ . The average speed is
Updated On: Apr 29, 2024
- $ 25\,km/h $
- $45 \,km/h$
- $ 55\,km/h $
- $ 75\,km/h $
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The Correct Option is B
Solution and Explanation
$=V_{a V}=\frac{\text { Total distance covered }}{\text { Total time taken }} $
$=\frac{\frac{x}{3}+\frac{2 x}{3}}{t_{1}+t_{2}}$
[Let the total distance covered is $x\, km$ ]
$=\frac{\frac{x}{3}+\frac{2 x}{3}}{\frac{\left(\frac{x}{3}\right)}{25}+\frac{\left(\frac{2 x}{3}\right)}{75}}$
$=\frac{x}{\frac{x}{75}+\frac{2 x}{225}}=\frac{x}{\frac{(3+2) x}{225}} $
$=\frac{225}{5}=45\, m / s$
$=\frac{\frac{x}{3}+\frac{2 x}{3}}{t_{1}+t_{2}}$
[Let the total distance covered is $x\, km$ ]
$=\frac{\frac{x}{3}+\frac{2 x}{3}}{\frac{\left(\frac{x}{3}\right)}{25}+\frac{\left(\frac{2 x}{3}\right)}{75}}$
$=\frac{x}{\frac{x}{75}+\frac{2 x}{225}}=\frac{x}{\frac{(3+2) x}{225}} $
$=\frac{225}{5}=45\, m / s$
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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.