Motion, a core principle of physics, entails the alteration of an object's position as time progresses. It is a key aspect of our everyday lives, as we observe objects moving or remaining at rest. To gain a clearer understanding of motion, it's important to examine the two fundamental states an object can be in—rest and motion.
An object is said to be at rest when it maintains the same position relative to its surroundings and shows no change in location over time. In other words, an object at rest remains stationary and does not exhibit any movement. It is important to note that the state of rest does not necessarily mean the absence of all motion at the microscopic level. Atoms and molecules within an object are constantly in motion, even when the object as a whole appears to be at rest.
On the other hand, the state of motion implies that an object is changing its position concerning its surroundings. This change can be described in terms of speed, direction, or both. An object in motion may travel along a straight path, move in a curve, rotate, or display a mix of these types of movements.
Displacement: In physics, displacement describes how far and in what direction an object has moved from its starting position to its ending point. It is a vector quantity, meaning it includes both the size of the movement (distance) and the direction. Displacement is commonly illustrated using an arrow that shows both the direction and magnitude of the motion.
Speed: Speed is a scalar quantity that measures how quickly an object moves. It represents the amount of distance covered over a specific period of time, without taking direction into account. To calculate speed, divide the total distance traveled by the time it took to travel that distance.
Speed:
Let Length = L
Time = T
Dimensional formula of Speed:
\(Speed = \frac{Displacement}{Time} = \frac{L}{T} = [LT^{-1}]\)
Unit of Speed: cm/s or m/s
Speed is measured in the International System of Units (SI) using meters per second (m/s).
Velocity: Velocity is a vector quantity that includes both speed and direction. It indicates how quickly an object moves in a specific direction and is determined by dividing the displacement by the time taken.
Let Length = L
Time = T
Dimensional formula of Velocity:
\(Velocity = \frac{Displacement}{Time} = \frac{L}{T} = [LT^{-1}]\)
Unit of Velocity: cm/s or m/s
Uniform Motion: Uniform motion refers to movement in a straight line at constant speed. An object in uniform motion covers equal distances in equal time intervals and does not experience acceleration or deceleration.
Acceleration: Acceleration describes how quickly the velocity of an object changes over time.
Let Length = L
Mass = M
Time = T
Distance = D
Acceleration:
\(a = \frac{Velocity}{Time} = \frac{V}{T} = \frac{\frac{D}{T}}{T} = \frac{D}{T^2}\)
Dimensional formula of Acceleration: \(\frac{L}{T^2} = [LT^{-2}]\)
Unit of Acceleration: cm/s² or m/s²
Retardation: Retardation is the rate at which velocity decreases with time. It is also known as negative acceleration.
If a body initially moves with velocity \(u\) and slows down to velocity \(v\) in time \(t\), where \(u > v\), then:
Retardation = \(\frac{u - v}{t} = -\frac{v - u}{t} = -a\)
(\(\text{Because } a = \frac{v - u}{t}\))
Dimensional formula of Retardation: \(\frac{L}{T^2} = [LT^{-2}]\)
Unit of Retardation: cm/s² or m/s²
Q1. A body had an initial velocity of 36 km/h and after 10 seconds, its velocity became 72 km/h. Find the acceleration of the body.
Solution:
Given:
Initial velocity, \(u = 36\) km/h = \(36 \times \frac{5}{9} = 20\) m/s
Final velocity, \(v = 72\) km/h = \(72 \times \frac{5}{9} = 40\) m/s
Time taken, \(t = 10\) s
Acceleration, \(a = ?\)
\(a = \frac{v - u}{t} = \frac{40 - 20}{10} = 2\) m/s²
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