Motion in One Dimension
One of the first lessons in Classical Mechanics is Motion in One Dimension. This article defines the concepts before demonstrating how they are used to describe various types of motion in one dimension. Motion is defined as a change in a body’s position in relation to its surroundings through time. Consider the motion of a body down a straight track to understand the notion of motion in one direction. In physics, a “body” is the subject of motion. A straight line, like that of a car on a straight road, is motion in one dimension. On her way to school along a straight highway, this driver encounters stoplights and different speed limits.
Motion in Two Dimensions
Two-dimensional (2D) motion is defined as motion that occurs simultaneously in two separate directions (or coordinates). An item travelling linearly in one dimension is the simplest motion. A car going down a straight route or a ball tossed straight up from the ground are both examples of linear movement. Calculating the motion of an item travelling in one direction at a constant velocity while accelerating in another is more difficult. Throwing a football or hitting a home run in baseball are both examples of 2D movement. The motion of the Earth’s gravitational field is investigated in the following instances in this chapter.
Motion in Three Dimensions
Three-dimensional motions refer to movements that take place in three dimensions. They might have a constant or changing velocity depending on the forces operating on them. Equations having three geographical variables and one temporal variable can be used to explain them. Kinetic energy may be found in every moving thing. All items in the cosmos move in three dimensions. The existence of a force is required for 3D movements. The existence of gravity causes 3D movements on a macroscopic scale in our cosmos. A 3D motion is demonstrated by the Sun’s orbit around the galactic centre. All objects in the cosmos have the ability to move in three dimensions. The tiny movements of the particles that make up matter (in any condition) are in three dimensions.
The shortest distance (x) a one-dimensional object is from a centre point, or origin, is defined as displacement. In a curved graph, displacement is shown versus time. A body can only move left and right when moving in one dimension. Consider a train travelling in a straight line. The origin is a point on that track, and the displacement is the distance between the origin and the body as it moves. If the displacement of our train, given the variable (x), is negative, the train is located |x| metres to the left of the origin. If (x) is greater than zero, the train is located x metres to the right of the origin. Consider a train travelling from point A to point B on a curved course. When the train arrives at B, the entire length of the curve will be the distance travelled. However, the train’s displacement will be the shortest distance between A and B, i.e. the length of the straight line between A and B.
The pace at which displacement varies over time is known as velocity. The quicker a body moves, the higher the velocity. It’s a vector quantity, which means it has both a magnitude and a direction. Velocity can be zero if the overall displacement is zero, which occurs only when the body comes to rest at the same position it started after travelling a specific distance in either direction. When the sign of the magnitude changes, the instantaneous velocity can also be zero; for example, a body experiencing constant acceleration in the opposite direction of travel will eventually switch directions and move in the direction of the acceleration, and its velocity will be zero at that point.
The rate at which velocity changes over time is called acceleration. A body moving with a positive acceleration increases its speed over time. Negative acceleration causes a body to lose velocity over time.
Motion with Constant Velocity
This is the most basic form of one-dimensional motion. If a body is sliding across a horizontal surface with negligible friction, it will have constant velocity motion. A puck sliding along a rink or a square block of ice sliding on a flat kitchen counter are two instances of objects with constant velocity motion. On the graph of displacement vs. time, motion with constant velocity is depicted. The velocity is calculated using the slope of the line on the graph, or dx/dt. The line’s equation is x = x0 + vt, where (x0) represents displacement, (v) represents velocity, and (t) represents time. The acceleration (a) in the equation is obviously equal to d2x/dt2, and “0,” because the body’s velocity is constant, and so neither growing nor decreasing.
Important question: Two particles A and B are projected from the same point with the same velocity of projection but at different angles alpha and beta of projection, such that the maximum height of A is two-third of the horizontal range of B. then which of the following relations are true?