Uniform and Non Uniform Motion

Motion is simply the change in an object's position over time. When something moves at a constant speed in a straight line—covering the same distance in equal intervals of time—that’s called uniform motion. For example, think of a car cruising steadily down a straight road.On the other hand, non-uniform motion happens when there’s a change in speed or direction. That means the object doesn’t cover the same distance in each time interval. A good example would be a car that’s speeding up or slowing down, or a ball that’s thrown into the air—it slows down as it goes up and speeds up as it comes down.

1.0Rest and Motion

1. Rest: An object is said to be at rest if it does not change its position with respect to its surroundings over time. Essentially, if an object’s position remains constant relative to a reference point, it is considered to be at rest. For example, a book lying on a table is at rest relative to the table.

2. Motion: It refers to the change in an object's position over time. An object is said to be in motion if its position is changing relative to a reference point.

Rest And Motion Are Relative

• Rest and motion are relative concepts because they depend on the observer's frame of reference. An object’s motion is described relative to something else. For instance, a person seated inside a moving car is at rest with respect to the car, but appears to be in motion when observed by someone standing outside. Similarly, a book on a table is at rest relative to the table, but in motion relative to the Earth, which is rotating.
• In essence, an object’s state of motion changes based on the observer’s point of view. There is no absolute state of rest or motion—everything is measured in relation to something else. 

2.0Uniform Motion

It is the motion of an object in which it travels equal distances in equal intervals of time, no matter how small the time interval is. In uniform motion, an object runs at a steady speed without changing direction. It just keeps going in a straight line at the same pace.

Key Points:

• The object moves in a straight line.
• Speed remains constant.
• Acceleration is zero.
• Velocity does not change with time.

3.0Non-Uniform Motion

It is the motion of an object in which it covers unequal distances in equal intervals of time. In this type of motion, the speed or direction (or both) of the object changes with time.

Key Points:

• Speed is not constant.
• There is acceleration or deceleration.
• Velocity changes over time.
• The motion may be in a straight or curved path.

Examples of Uniform and Non-uniform Motion

5.0Equations of Motions (Graphical Method)

(1) v=u+at

a=slope of graph $\Rightarrow$ Acceleration

$a=\frac{BE}{EA}=\frac{BD-DE}{OD}=\frac{v-u}{t}\Rightarrow v=u+at$

(2) $s=ut+\frac{1}{2}a{t}^2$

From velocity-time graph

$a=\frac{BE}{EA}\Rightarrow BE=at$

$s=\text{ar}(\square OAED)+\text{ar}(△ABE)$

$s=OD\times ED+\frac{1}{2}\times AE\times BE$

$s=t\times u+\frac{1}{2}\times t\times at$

$s=ut+\frac{1}{2}a{t}^2$

(3) $v^2=u^2+2as$

$s=\text{ar}(\text{trapezium})\square ABD$

$=\frac{1}{2}\times (BD+OA)\times OD$

$=\frac{1}{2}(v+u)\times OD$

$a=\frac{BE}{EA}=\frac{BD-ED}{OD}=\frac{BD-ED}{a}$

$s=\frac{1}{2}(v+u)\times \left(\frac{v-u}{a}\right)$

$s=\frac{v^2-u^2}{2a}\Rightarrow v^2=u^2+2as$

$v^2-u^2=2as\Rightarrow v^2=u^2+2as$

Example-1.A car accelerates uniformly along a straight road, passing points P and Q with speeds of 30 km/h and 40 km/h, respectively. What is its speed at the midpoint between P and Q?

Solution:

Between points P and M

$v_m^2=30^2+2a(d)$

$2ad=v_m^2-900$……(1)

Between points M and Q

$40^2=v_m^2+2a(d)$

$2ad=1600-v_m^2$……(2)

From equations (1) and (2)

$v_m^2-900=1600-v_m^2$

$2v_m^2=2500\Rightarrow v_m=\sqrt{\frac{2500}{2}}km/hr$

Example-2:Two cars start off a race with velocities 2m/s and 4m/s travel in a straight line with uniform accelerations $2m/s^2$ and $1m/s^2$  respectively. What is the length of the path if they reach the final point at the same time?

Solution:

For 1st particle $s=4(t)+\frac{1}{2}(1)t^2=4t+\frac{t^2}{2}$

For 2nd particle $s=2(t)+\frac{1}{2}(2)t^2=2t+t^2$

Equating above equations

$4t+\frac{t^2}{2}=2t+t^2\Rightarrow t=4s$

Substituting value of t in above equations

$s=4(4)+\frac{1}{2}(1)4^2=16+8=24m$

6.0Uniform and Non-Uniform Circular Motion

Uniform Circular Motion (UCM): An object moving at an unchanged speed along a circular path experiences a continuous change in velocity because its direction is constantly changing, even though its speed remains the same.

Key Characteristics:

• Speed is constant
• Velocity alters due to the change in direction
• Acceleration is present (called centripetal acceleration)
• Centripetal Force is required to keep the object in circular motion, directed towards the center of the circle

Non-Uniform Circular Motion: It occurs when an object moves in a circular path, but its speed is changing — that is, it is accelerating or decelerating along the circular path.

Key Characteristics:

• Speed is changing (increasing or decreasing)
• Both magnitude and direction of velocity change
• There are two components of acceleration:

1. Tangential acceleration (at): due to change in speed
2. Centripetal acceleration (ac): due to change in direction

7.0Examples of Uniform and Non-uniform Circular Motion