Motion in Plane with Constant Acceleration

We define acceleration to be the rate of change of velocity

The athletic sprint is a good example of acceleration.

Acceleration of an object is defined to be the rate of change of velocity of that object

Mathematically, $\text{Acceleration}=\frac{\text{Change in Velocity}}{\text{Change in Time}}$

The runners start from rest and in the next few instants, they change their velocity. Hence, they accelerate

The vehicle is also accelerating as it moves through the crest and trough

We shall now discuss examples of motion in plane with constant acceleration

The most common example of motion in plane with constant acceleration is the projectile motion

This is the basic approximation of the trajectory of an object undergoing projectile motion

Here we see that an object following such a trajectory, has displacements both in the x & y plane

That's why the projectile motion is put under the category of Motion in a Plane

Applications of projectile motion include catapult

The trajectory of the ball after it has been hit for a six by a batsman also roughly follows projectile motion

The motion of a basketball as it enters the basket is an example of projectile motion

The acceleration of any object undergoing motion in a plane can be resolved into two components

Component of Acceleration in x-plane -$a_x$ Component of Acceleration in y-plane -$a_y$

$a_x$ is responsible for the motion of the object in only x-direction

$a_y$ is responsible for the motion of the object in only y-direction

The resultant acceleration can be obtained from the vector rule of resultant

$\vec{a}$ = ${\vec{a}}_x+{\vec{a}}_y$ $\left|\vec{a}\right|=\sqrt{a_x^2+a_y^2}$

But when a body is undergoing projectile motion, the only acceleration is in the y-axis

It is the Acceleration due to Gravity. It is the only acceleration acting on a body undergoing projectile motion

Therefore, Projectile Motion is categorized under Motion with Constant Acceleration

We can thus say, $a_x=0$ and $a_y=g$ (We have considered the downward direction as positive)

Revision

Acceleration is defined as the rate of change of velocity. For motion in a plane, the acceleration can be resolved into two components

The most common example of Motion in a Plane is the Projectile Motion. Few examples are; the motion of a basketball into the basket, catapult, cricket ball being hit for six etc

There is only one component of acceleration in Projectile Motion, which is the Acceleration due to Gravity. Hence, projectile motion has a constant acceleration

The End