Two particles P and Q get 5 m closer each second while travelling in opposite direction. They g

Two particles P and Q get 5 m closer each second while...

Two particles $\mathrm{P}$ and $\mathrm{Q}$ get $5 \mathrm{~m}$ closer each second while travelling in opposite direction. They get $1 \mathrm{~m}$ closer each second while travelling in same direction. The speeds of $\mathrm{P}$ and $\mathrm{Q}$ are respectively (A) $5 \mathrm{~ms}^{-1}, 1 \mathrm{~ms}^{-1}$ (B) $3 \mathrm{~ms}^{-1}, 4 \mathrm{~ms}^{-1}$ (C) $3 \mathrm{~ms}^{-1}, 2 \mathrm{~ms}^{-1}$ (D) $10 \mathrm{~ms}^{-1}, 5 \mathrm{~ms}^{-1}$

Two particles $\mathrm{P}$ and $\mathrm{Q}$ get $5 \mathrm{~m}$ closer each second while travelling in opposite direction. They get $1 \mathrm{~m}$ closer each second while travelling in same direction. The speeds of $\mathrm{P}$ and $\mathrm{Q}$ are respectively
(A) $5 \mathrm{~ms}^{-1}, 1 \mathrm{~ms}^{-1}$
(B) $3 \mathrm{~ms}^{-1}, 4 \mathrm{~ms}^{-1}$
(C) $3 \mathrm{~ms}^{-1}, 2 \mathrm{~ms}^{-1}$
(D) $10 \mathrm{~ms}^{-1}, 5 \mathrm{~ms}^{-1}$

Key Concepts

Relative Motion

Relative motion refers to the calculation of the motion of an object with respect to another moving object. It involves using the concept of relative speed, which determines how fast two objects are moving towards or away from each other based on their individual speeds.

Relative Speed in Opposite Directions

When two objects move in opposite directions, their relative speed is the sum of their individual speeds. This is because the distance between them decreases at a rate equal to the sum of their speeds.

Relative Speed in Same Direction

When two objects are moving in the same direction, the relative speed is the difference between their individual speeds. This measures how quickly the distance between them changes.

Setting Up Equations

In problems involving relative motion, equations can be established using the relationships between the relative speed when moving in the same direction (difference of speeds) and in opposite directions (sum of speeds). Solving these simultaneous equations allows for the determination of the individual speeds of the objects.

Transcript

00:01 Hello students, our question is two particles p and q get 5 meters closer each second while traveling in opposite direction.

00:12 They get 1 meter closer each second while traveling in the same direction.

00:17 The speed of particle p and q are respectively.

00:21 So we have to find the speed of particle p and q.

00:25 So let's start our solution.

00:27 First we will try to make a diagram of it.

00:30 Suppose this is our particle teeth and this is our particle tube.

00:38 This is our particle tube.

00:40 When they are moving in opposite direction, particle t is moving in this direction.

00:45 Particle t is moving in this direction.

00:48 So they are 5 meters closer when they are moving in opposing direction.

00:56 So in the second case, this is first case, in the second case there are one meter apart that is this is particle p particle p i will make it this is our particle p and this is our particle they are one meter apart one meter then they are moving in the same direction particle is moving in this direction and particle is moving in this so we use the concept of relative speed so when they are moving in opposite direction in this case, the relative speed of particle p with respect to q is equal to speed of particle p plus speed of particle.

01:56 So the distance between the two particles is 1 meter, a speed is equal to distance over time.

02:06 When distance in this case is 5 meter time is 1 second, it is equal to speed of particle p plus speed of particle 2.

02:18 The speed of particle p plus speed of particle 2 is equal to 5.

02:25 This is a vibrating 1...

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