Motion in a Plane     Motion in a Plane Introduction

A body moving from one point to different points on the X and Y-axis is said to be executing motion in a plane. A plane comprises the X and Y-axis on which if we make the distance at the X-axis and the time at which a body moves along the vertical or Y-axis, then the dividing the distance covered by the time taken we get the velocity

Similarly, on plotting the velocity along the X-axis and the time at the Y-axis and the product so obtained is the acceleration of the body.

Here, we will discuss all motion in a plane with its detailed introduction and formulas.

Parameters of Motion in a Plane

In the above heading, we discussed three parameters of motion, viz: distance, velocity, acceleration; besides these three, we have a displacement as well. Now, let’s introduce the concept of a motion in a plane in detail:

For understanding motion in a plane, it is necessary to understand motion in one dimension and the following parameters of motion in detail.

Distance:

It is an overall measurement of the body that is calculated from the point an object initiates its journey to the point it terminates its journey. It is a scalar physical quantity, so we won’t be sure of in which direction we are travelling along with the train, we just know the distance we covered from Delhi to Bangalore.

Time:

We are moving along with the time, so a factor through which we can determine the velocity and acceleration of an object is the time; however, it is a scalar quantity, so we just know the time we would reach Delhi from Dehradun, not the direction the train takes.

Velocity:

It is a physical quantity that describes the magnitude and direction of a moving object. A velocity demonstrates how an object can be defined as the rate of change of the object’s position with respect to a frame of reference and time. Well! It might sound complicated because velocity is basically the speed of an object in a specific direction.

Displacement:

It is also a physical quantity that describes both the magnitude and direction of a body executing motion; however, it is the shortest distance a body can take reaching from one point to another.

Motion in a Plane

We already know that velocity is a vector quantity, and therefore, by Pythagoras theorem, the magnitude of the velocity vector is given by:

।v। = v = $\sqrt{vx^{2} + vy^{2}}$....(1)

Since we are considering motion in a plane, so we determined the velocity along both the axis and then calculated the magnitude of a velocity vector by applying the Pythagoras theorem.

For acceleration along both the axis, we have the following two equations:

ax  = $\frac{dvx}{dt}$ ….(2)

ay  = $\frac{dvy}{dt}$ ….(3)

Motion in Plane Equations

v= u + at…..(4)

s = ut + ½ at² …..(5)

v² = u² + 2as …..(6)

Here, equations (4), (5), and (6) are motion in a plane formulas for a particle ‘P’ executing motion in a plane, let’s define these one-by-one:

u = initial velocity

v = final velocity

s = displacement of particle ‘P’

t = time the particle takes while executing a motion

a = acceleration of the particle executing motion in a plane

For a particle moving along the X and Y-axis, the above equations: (4), (5), (6) becomes in the following manner:

For X-axis:

vx   = u + ax

s = uxt + ½ axt²

vx² = ux² + 2axs

The definition also changes in the following way:

u = initial velocity along the X-axis

v = final velocity along the X-axis

s = displacement of particle ‘P’ along the X-axis

t = time the particle takes while executing a motion along the X-axis

a = acceleration of the particle executing motion in a plane along the X-axis

Now, for Y-axis:

vy   = u + ay

s = uyt + ½ ayt²

vy² = uy² + 2ays

The definition also changes in the following way:

u = initial velocity along the Y-axis

v = final velocity along the Y-axis

s = displacement of particle ‘P’ along the Y-axis

t = time the particle takes while executing a motion along the Y-axis

a = acceleration of the particle executing motion in a plane along the Y-axis

Now, let’s see some examples of real-life objects making a motion in a plane:

Examples of 2-D Motion in a Plane

• Throwing a cricket ball or a cannonball.

• The motion of a billiard ball along with the floor of the billiard table.

• A downstream or upstream motion of a boat in a river.

• A circular motion/revolution of the Earth around the Sun.

• A projectile motion of a bullet fired from a gun

Projectile motion is one of the best examples of an object bearing motion in a plane; let’s discuss it:

The equation for the body executing a projectile motion is:

y = ax + bx² …..(7)

Question 1: What is Motion in a Plane Class 11?

Answer: Motion in a Plane Class 11 comes under the subject Physics Chapter 4. Motion in a plane is called a motion in two dimensions. Its examples are projectile motion, circular motion. For the analysis of such motion, our reference is an origin and two co-ordinate axes viz: X and Y-axis and scalar and vector physical quantities.

Question 2: What is an Example of Motion in a Plane?

Answer: The motion of an object in a plane gives us equations of its motion along the axes or two dimensions. For the X-axis: One of the most common examples of motion in a plane is Projectile motion. In a projectile motion, the only acceleration acts on the object in the vertical direction which is actually the acceleration due to gravity (g), i.e., 9.8 ms⁻².

Question 3: How Do We Study the Motion in a Plane?

Answer: We study the motion in a plane with the help of topics like vectors, projectile motion, displacement, acceleration, time, relative motion, and many more physical quantities. In a plane, we apply the same equations of motion separately in both directions: X -xis and Y-axis.

Question 4: What is Two-dimensional Projectile Motion?

Answer: In a 2-D projectile motion, throwing a rock or kicking a football ball generally produces a projectile pattern of motion that has both a vertical and a horizontal component.

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