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What Is Two-Dimensional Motion?

Constant Velocity

A moving item with constant velocity must move at the same pace and in the same direction. Constant velocity motion is one of the most fundamental forms of motion. Similar to a hockey puck sliding over the ice, this sort of motion happens when an item moves (or slides) in the presence of little or no friction. To have a constant velocity, an item must move at a constant speed in a constant direction. When an item 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. External forces should not be applied to the item if the acceleration is zero. This may be mathematically represented as follows:

a = dv/dt = 0 ⇒ v =const.

The graph of distance vs. time (x vs. t) illustrates the same change in position throughout each period of time if an item is travelling at constant velocity. As a result, an item moving at constant velocity is represented as a straight line:
x = x0 + vt, where x0 is the displacement when t = 0 (or at the y-axis intercept). If you know an object’s trace through time, you can also get its velocity. We can compute velocity from the change in distance over time given a graph like this. The slope of the line can be read as the velocity in graphical terms. The sign of our slope indicates whether the velocity is positive or negative. This indicates which way the item is moving.

Constant Acceleration

The object is referred to as a projectile, and the path it follows is referred to as a trajectory. The motion of falling items is a straightforward one-dimensional projectile motion with no horizontal movement. There is a vertical and a horizontal component to two-dimensional motion, such as that of a football or other thrown item. The most important thing to remember is that motion along perpendicular axes is independent of one another and so may be examined separately.

Breaking down two-dimensional projectile motion into two movements, one along the vertical axis and the other along the horizontal axis is the key to understanding it. We must include velocity, acceleration, and displacement when describing motion. All forces other than gravity (such as air resistance and friction, for example) will be assumed to be insignificant. The components of acceleration are therefore rather straightforward: ay = −g = −9.81m/s2 (we assume that the motion occurs at small enough heights near the surface of the earth). Because gravity’s acceleration is exclusively in the vertical direction, axe = 0. Thus, the following kinematic equations may 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 investigate it, we divided two-dimensional projectile motion into two one-dimensional motions along the vertical and horizontal axes. Because axe = 0 and hence vx is constant, horizontal motion is easy. As an item climbs, its vertical velocity begins to diminish; at its greatest point, the vertical velocity is zero. The vertical velocity of an item as it descends towards the Earth grows in magnitude but points in the opposite direction of the starting vertical velocity. The overall velocity may be calculated by combining the x and y movements at any point along the trajectory.

Key Points

  • The term “constant velocity” refers to an item travelling in a straight path at a constant speed.
  • This line may 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 our slope indicates whether the velocity is positive or negative. This indicates which way the item is moving.
  • Motion that does not alter in speed or direction is referred to as constant velocity.
  • In two dimensions, constant acceleration in motion typically follows a projectile pattern.
  • The motion of an item launched or projected into the air, subject exclusively to gravity’s (vertical) acceleration, is known as projectile motion.
  • kinematic: pertaining to or involving motion or kinematics.

Important Question: A ball rolls off the top of a staircase with a horizontal velocity u m s^-1. If the steps are h metre high and b mere wide, the ball will just hit the edge of n-th step. Find the value of n.?

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