June 25, 2017

Particle Motion

Let's discuss a beautiful problem useful for Physics Olympiad based on Particle Motion.

The Problem: Particle Motion

A particle Q is moving +Y axis. Another particle P is moving in XY plane along a straight line x=-d (d>0) with a uniform speed v parallel to that of Q. At time t=0, particles P and Q happen to be along X-axis whereas a third particle R situated at x=+d starts moving opposite to P with a constant acceleration a. At all further instants, the three particles happen to be collinear. Then Q

(A) has an initial speed v/2

(B)will come to rest after a time interval v/a

(C)has an acceleration –a/2

(D) will return to its initial position after a time interval 2v/a

Discussion:

$$y_2-y_1=\frac{y_2-y_1}{x_2-x_1}(x_2-x_1)$$
$$ y-vt=\frac{\frac{-1at^2}{2}-vt}{2d}(x+d)$$
On differentiating  taking x=0
$$v'-v=\frac{-at-v}{2d}(d)$$

At t=0,
$$ v'-v=\frac{0-v}{2}....(i)$$.
$$\Rightarrow v'=\frac{v}{2}$$
For $$v'=0,$$

we have,
$$ 0-v=\frac{-at-v}{2}$$
$$ \Rightarrow t=\frac{v}{a}$$
Differentiating (i)
$$ a'-0=\frac{-a}{2}$$
$$\Rightarrow a'=\frac{-a}{2}$$

Hence, the correct options will be a,b,c,d.

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com