A moving object with a constant rate should move at a constant pace and in the same direction. Constant rate motion is one of the most basic types of motion. Like a disk sliding over ice, this type of motion happens when an object moves (or slides) in the presence of very little or no friction.
To have a constant rate, an object must move at a constant speed in a constant direction. When an object has a consistent direction, it can only move in a straight line.
Newton’s second law states that when a force is applied to an object, it will accelerate. No external forces should be applied to the object if the acceleration is zero. This can be mathematically described as follows:
a = dv/dt = 0 → v = const.
A graph of distance vs. time (x vs. t) illustrates a constant change in position over every interval of time if an object is traveling at a constant rate. As a result, an object moving at a constant rate is described by a straight line:
x = x0 + vt, where x0 is the displacement when t = 0 (i.e., the y-axis intercept). If you know an object’s position over time, you can also find its velocity. We can calculate the velocity from the change in distance over time using a graph like this.
The slope of the line is read as the velocity in graphical terms. The sign of the slope indicates whether the velocity is positive or negative, which tells you the direction the object is moving.
Constant Acceleration
The object is called a projectile, and the path it follows is called its trajectory. The motion of a falling object is a simple one-dimensional projectile motion with no horizontal movement. There’s a vertical and a horizontal component to two-dimensional motion, like that of a thrown ball or other projected object.
The most important thing to remember is that motion on perpendicular axes is independent of one another, so each can be examined separately. Breaking down two-dimensional projectile motion into two movements — one on the vertical axis and the other on the horizontal axis — is the key to understanding it.
We should include velocity, acceleration, and displacement when describing motion. All forces aside from gravity (such as air resistance and friction) will be assumed to be insignificant.
The components of acceleration are fairly straightforward: ay = −g = −9.81 m/s² (assuming the motion happens at sufficiently small heights near the Earth’s surface). Since gravity’s acceleration is only in the vertical direction, ax = 0. So the following kinematic equations can be used to describe motion in the x and y directions:
x = x0 + vxt
vy = v0y + ayt
y = y0 + v0yt + 1/2ayt²
v²y = v²0y + 2ay(y−y0)
To analyze it, we divide two-dimensional projectile motion into two one-dimensional motions on the vertical and horizontal axes.
Since ax = 0, and vx is therefore constant, horizontal motion is straightforward. As an object climbs, its vertical velocity begins to decrease; at its highest point, the vertical velocity is zero.
The vertical velocity of an object as it descends toward the ground grows in magnitude but points in the opposite direction of the starting vertical velocity. The velocity can be calculated by combining the x and y movements at any point along the trajectory.
Key Points
The term “constant velocity” refers to an object traveling along a straight path at a constant speed.
This can also be written algebraically as x = x0 + vt, where x0 denotes the object’s location at t = 0, and the slope denotes the object’s speed.
The sign of the slope indicates whether the velocity is positive or negative, which tells you the direction the object is moving.
Motion that doesn’t change in speed or direction is called constant rate motion.
In two dimensions, constant acceleration generally produces a projectile pattern of motion.
The motion of an object launched or projected into the air, subject only to gravity’s (vertical) acceleration, is known as projectile motion.
Kinematics: relating to or involving motion or mechanics.
Practice question: A ball rolls off the top of a staircase with a horizontal velocity of u m/s. If the steps are h meters high and b meters wide, the ball will hit the edge of the nth step. Find the value of n.
