Introduction To Motion In Two Dimensions
We have learned about motion in a straight line and the three equations of motion. Now we will learn about motion in a plane. When we are talking about motion in a plane, we are actually talking about motion in two dimensions, since two dimensions make a plane. So we are taking two axes into consideration, generally Xaxis and Yaxis. In order to derive equations of motion, we need to know about motion in one dimension.
Study the motion in a plane with the help of topics like vectors, projectile motion, relative motion and more.
The equations of motion in a straight line are:

Where,
 v = final velocity of the particle
 u = initial velocity of the particle
 s = displacement of the particle
 a = acceleration of the particle
 t = time interval in which the particle is in consideration
In a plane, we have to apply the same equations separately in both the directions: Y axis and Yaxis.
This would give us the equations for motion in a plane:

Where,
 v_{y}= final velocity of the particle in y direction
 u_{y}= initial velocity of the particle in y direction
 s_{y}= displacement of the particle in y direction
 a_{y}= acceleration of the particle in y direction
 t = time interval in which the particle is in consideration
Similarly, for Xaxis:

Where,
 v_{x}= final velocity of the particle in x direction
 u_{x}= initial velocity of the particle in x direction
 s_{x}= displacement of the particle in x direction
 a_{x}= acceleration of the particle in x direction
 t = time interval in which the particle is in consideration
Relative Motion
When we say the motion of body A relative to B we mean motion of A, as observed from B’s frame of reference. Mathematically it is represented as:
Where,
 V_{BA} = Velocity of B as observed from A.
 V_{B} = Velocity of B from the earth as the reference frame.
 V_{A} = Velocity of A from the earth as the reference frame.
Watch this video to have a better and visual understanding of motion in a plane.
Consider a man running uphill while it is raining. It is difficult to decide from which side the man will get wet if we do not know the relative m of the man and rain with respect to each other. Suppose, the components of velocity of man are given as 6i + j and that of rain is given by 3i – 3j. If we can find the angle at which the rain hits the man, we can easily decide from which direction the man gets hit by the rain. To find the relative velocity or relative motion of rain with respect to man, the velocity of a man with respect to rain must be subtracted, i.e.,

Relative motion can be explained using the vector representation as:
It can be seen that with respect to the man, the rain is falling at an angle of \(tan^{1} \left( \frac 34 \right)\) .. So, if the man is running in positive X direction then rain must hit him from the front direction. So, if the man has to wear a bag he must wear it on his back to prevent it from rain. Thus only by knowing the velocities, the direction of hitting of rain can be determined. Now, what happens if the horizontal component of the velocity of rain and man becomes equal? Interesting, isn’t it? Well, in such a situation the rain won’t hit the man from either side. So, to answer the question of whether one should run fast or slow in the rain to get less wet, it all depends on the velocities or relative motion.
Projectile Motion
Projectile motion is one of the most common examples of motion in a plane. In projectile motion, the only acceleration acting is in the vertical direction which is acceleration due to gravity (g). Therefore, equations of motion can be applied separately in Xaxis and Yaxis to find the unknown parameters. To know more about projectile motion watch the video give below:
Frequently Asked Questions on Motion In A Plane
What is motion in a plane?
Motion in a plane means motion in a twodimensional plane which includes xaxis and yaxis.
What is onedimensional motion and twodimensional motion?
When the object travels in a straight line irrespective of the direction is known as onedimensional motion. When the object travels in x and y coordinates with a constant velocity it is known as twodimensional motion.
What is accelerated motion?
When the velocity is increased gradually with respect to the time it is known as accelerated motion.
What is oscillatory motion?
The to and fro motion of the object about its mean position is known as oscillatory motion.
What is projectile motion?
Projectile motion is when the object is projected into air and gravity is the only force acting upon the object.
Hope you have got a brief insight of motion in a plane of motion in two dimensions. Learn more about other related concepts of physics and their applications, with interactive videos by visiting BYJU’S.