Important Relative Motion Formulas for JEE Main and Advanced

Relative motion is a combined property of the object under study as well as the observer. There is no such thing as absolute motion or absolute rest. Motion is always defined with respect to an observer or reference frame. Having said that, here on this page, students will find a list of relative motion formulas which will further boost their revision before the entrance exams.

Relative Motion in One Dimension

1. Relative Position

Here,

2. Relative Velocity

Here,

3. Relative Acceleration

It is the rate at which relative velocity is changing

4. Equation of motion (if relative acceleration is constant)

v = u + at

S = ut + (1/2)at²

v² = u² + 2as

5. Velocity of Approach/Separation

It is the component of the relative velocity of one particle w.r.t another along the line joining them. If the separation is decreasing, we say it is the velocity of approach, and if separation is increasing, then we say it is the velocity of separation.

Relative Motion in two Dimension

Here,

Here,

Here,

Relative Motion in River Flow

Consider a man swimming in a river with velocity V_MR relative to the river at an angle of θ with the river flow. The velocity of the river is V_R. Let us consider 2 observers (observer 1 and observer 2). Observer 1 is on the ground, and observer 2 is in a raft floating along with the river. Therefore the motion w.r.t to observer 2 is the same as the motion w.r.t to the river. The man will flow with angle θ with the river flow for observer 2. For observer 1, the velocity of the river will be V_M=V_MR + V_R. Therefore the swimmer will appear to move at an angle θ’ with the river flow.

1. Drift

It is defined as the displacement of the man in the direction of the river flow. In the figure above x is the drift.

2. Crossing the river in the shortest time

Time to cross the river will be minimum if man swims perpendicular to the river flow

T_min = d/V_MR

3. Crossing the river in the shortest path, Minimum drift

The minimum possible drift is zero. In this case, the man swims in the direction perpendicular to the river flow as seen from the ground. This path is known as the shortest path. For minimum drift, the man must swim at some angle Φ with the perpendicular in a backward direction, which is given by sin Φ = V_R/V_MR

Time to cross the river along the shortest path

t = d/V_MR cos Φ

Wind Airplane Problem

The velocity of the aeroplane with respect to the wind is

Here

Rain Problem

The rain is falling vertically with a velocity V_R and the observer is moving horizontally with velocity V_M, the velocity of rain relative to an observer will be

And direction θ = tan^-1(V_m/V_R)

Up Next: Important Work, Power and Energy Formulas For JEE

Relative Motion Videos

Rain Man Problem