How to Prepare Motion in A Straight Line and Plane for the Test?

Motion in a plane is defined as a body moving from one point to various points on the X and Y axes. The X and Y axes make up a plane, and if we measure the distance travelled along the X-axis and the time it takes for a body to move along the vertical or Y-axis, we can calculate velocity by dividing the distance travelled by the time it takes. Similarly, the product produced by graphing the velocity along the X-axis and the time along the Y-axis is the body’s acceleration. All motion in a plane will be discussed here, along with a comprehensive introduction and formulae.

Motion Parameters in a Plane

We covered three motion characteristics in the previous heading: distance, velocity, and acceleration; in addition to these three, we have a displacement. Let’s take a closer look at the notion of motion in a plane: Understanding motion in one dimension and the following motion characteristics in depth is required to comprehend motion on a plane.

Distance

It is a whole- body measurement that is computed from the point where an object begins its journey to the place where it ends it. We won’t know the direction we’re travelling with the train since it’s a scalar physical quantity; all we’ll know is the distance we travelled from Delhi to Bangalore.

Time

Because we move with the passage of time, we may use it to calculate an object’s velocity and acceleration; but, because time is a scalar number, we only know how long it will take us to go to Delhi from Dehradun, not which direction the train will travel.

Velocity

A moving object’s magnitude and direction are described by this physical quantity. A velocity shows how an object’s location may be described as the rate of change of its position in relation to a frame of reference and time. Well! Because velocity is the speed of an item in a given direction, it may appear complex.

Displacement

Displacement is a physical number that defines both the size and direction of a body’s motion; nonetheless, it is the minimum distance a body may travel in order to reach another location.

Motion in a Plane

We already know that velocity is a vector quantity, thus the magnitude of the velocity vector is determined by Pythagoras theorem:

।v। = v =    (1)

We computed the velocity along both axes and then used the Pythagoras theorem to calculate the magnitude of a velocity vector because we are examining motion in a plane. We have the following two equations for acceleration along both axes:

a_x = dvx/dt    (2)

a_y = dvy/dt    (3)

Motion in Plane Equations

v= u + at      (4)

s = ut + ½ at²         (5)

v² = u² + 2as          (6)

Let’s define equations (4), (5), and (6), which are motion in a plane formulae for a particle ‘P’ performing motion in a plane, one by one: u = initial velocity; v = final velocity; s = displacement of particle ‘P’; t = the amount of time it takes for a particle to complete a motion; a = the acceleration of a particle moving in a plane; The aforementioned equations: (4), (5), (6) become as follows for a particle travelling along the X and Y axes:

For X-axis:

v_x   = u + a_xt 

s = u_xt + ½ axt²

vx² = ux² + 2a_xs

The following adjustments are made to the definition. u denotes the initial velocity on the X-axis; v represents the final velocity along the X-axis; s is the displacement of particle ‘P’ along the X-axis; t is the amount of time it takes for a particle to move along the X-axis; a is the particle’s acceleration when moving in a plane along the X-axis.

Now, for Y-axis:

v_y   = u + a_yt 

s = u_yt + ½ ayt²

vy² = uy² + 2a_ys

The following adjustments are made to the definition: u denotes the initial velocity on the Y-axis; v represents the final velocity along the Y-axis.; s is the particle ‘P’ displacement along the Y-axis; t is the amount of time it takes for a particle to move down the Y-axis; a is the acceleration of a particle moving in a plane parallel to the Y-axis. Let’s look at some examples of real-world things moving on a plane.

2-D Motion in a Plane Examples

Cannonballing or throwing a cricket ball. The movement between a billiard ball and the billiard table’s floor. A boat moving downstream or upstream in a river. The Earth revolves around the Sun in a circular9 manner. A bullet’s projectile motion when fired from a gun. One of the greatest examples of object carrying motion in a plane is projectile motion. The body conducting a projectile motion has the following equation:

y = ax + bx² (7) Interesting question: A cricketer can throw a ball to a maximum horizontal distance of 100 m. How high above the ground can the cricketer throw the same ball?

 

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