Question:
A car moving with a speed of $50 \,km\, h^{-1}$ can be stopped by applying brakes after moving atleast $6 \,m$. If the same car is moving at a speed of $100 \,km\, h^{-1}$ the minimum stopping distance is
A car moving with a speed of $50 \,km\, h^{-1}$ can be stopped by applying brakes after moving atleast $6 \,m$. If the same car is moving at a speed of $100 \,km\, h^{-1}$ the minimum stopping distance is
Updated On: Jun 6, 2024
- $ 12\,m $
- $ 18\,m $
- $ 6\,m $
- $ 24\,m $
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The Correct Option is D
Solution and Explanation
Case I. $v^{2}=u^{2}-2 a s$
$0=(50)^{2}-2 \times a \times \frac{6}{1000}$
$\frac{2 \times a \times 6}{1000}=50 \times 50$
$a=\frac{50 \times 50 \times 1000}{2 \times 6}$
Case II. $v^{2}=u^{2}-2 a s$
$0=(100)^{2}-2 \times \frac{50 \times 50 \times 1000}{2 \times 6} \times 5$
$s=\frac{100 \times 100 \times 6}{50 \times 50 \times 1000}$
$s=\frac{24}{1000} km$
$s=24 \,m$
$0=(50)^{2}-2 \times a \times \frac{6}{1000}$
$\frac{2 \times a \times 6}{1000}=50 \times 50$
$a=\frac{50 \times 50 \times 1000}{2 \times 6}$
Case II. $v^{2}=u^{2}-2 a s$
$0=(100)^{2}-2 \times \frac{50 \times 50 \times 1000}{2 \times 6} \times 5$
$s=\frac{100 \times 100 \times 6}{50 \times 50 \times 1000}$
$s=\frac{24}{1000} km$
$s=24 \,m$
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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.