Question:
A person walks up a stationary escalator in time $t_1$. If he remains stationary on the escalator, then it can take him up in time $t_2$. How much time would it take him to walk up the moving escalator?
A person walks up a stationary escalator in time $t_1$. If he remains stationary on the escalator, then it can take him up in time $t_2$. How much time would it take him to walk up the moving escalator?
Updated On: Jun 7, 2022
- $ \frac{t_1 + t_2}{2}$
- $\sqrt{t_1 t_2}$
- $ \frac{t_1 t_2}{t_1 + t_2}$
- $ t_1 +t_2$
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The Correct Option is C
Solution and Explanation
Let $L$ be the length of escalator.
Speed of man w.r.t. escalator is $v_{mc} = \frac{L}{t_1}$
Speed of escalator is $v_c = \frac{L}{t_2}$
$ \therefore $ Speed of man with respect to ground would be
$ v_m = v_{mc} + v_c = L \left( \frac{1}{t_1} + \frac{1}{t_2} \right)$
$\therefore$ Time taken $t = \frac{L}{L\left(\frac{1}{t_{1}}+\frac{1}{t_{2}}\right)}=\frac{t_{1}t_{2}}{t_{1}+t_{2}}$
Speed of man w.r.t. escalator is $v_{mc} = \frac{L}{t_1}$
Speed of escalator is $v_c = \frac{L}{t_2}$
$ \therefore $ Speed of man with respect to ground would be
$ v_m = v_{mc} + v_c = L \left( \frac{1}{t_1} + \frac{1}{t_2} \right)$
$\therefore$ Time taken $t = \frac{L}{L\left(\frac{1}{t_{1}}+\frac{1}{t_{2}}\right)}=\frac{t_{1}t_{2}}{t_{1}+t_{2}}$
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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.