First slide

The 3 equation for uniform acc

Question

A passenger is at a distance x from a bus, when the bus begins to move with a constant acceleration a. What is the minimum velocity with which the passenger should run towards the bus so as to catch it ?

Moderate

A

$\sqrt{(2 ax)}$
B

2ax
C

ax
D

$\sqrt{(ax)}$

Solution

Let v be the velocity of the passenger and the passenger catches the bus after a time t. Then, the distance covered by both is same. Hence
$vt = x + \frac{1}{2} {at}^{2}$
or ${at}^{2} â 2 vt + 2 x = 0$
$â´$ $t = \frac{+ 2 v Â\pm \sqrt{(4 v^{2} â 8 ax)}}{2 a}$
$= \frac{v Â\pm \sqrt{(v^{2} â 2 ax)}}{a}$
t is real, when v² - 2 a x is positive or zero. Hence minimum speed is given by
v² -2ax=0
$â´ v = \sqrt{(2 ax)}$

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