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Linear Motion

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Physics

In the realm of physics, linear motion occurs when an object's acceleration and velocity are in one dimension, meaning just horizontal motion, just vertical motion, or just motion along a line of some other direction. Unbalanced forces are what cause an object to accelerate. The acceleration of gravity on earth is -9.81 meters per second squared. A falling object will accelerate at this rate until it reaches terminal velocity, where the force of air resistance is equal and opposite to the force of gravity.

There are four kinematic equations that describe linear motion with constant acceleration: (1) vf = vi + a*t (Velocity = initial velocity + acceleration x time), (2) d = vi*t + 0.5*a*t^2 (Displacement = initial velocity x time + acceleration x time squared / 2), (3) vf^2 = vi^2 + 2*a*x (Velocity squared = initial velocity squared + 2 x acceleration x displacement), and (4) x = 0.5*(vi + vf)*t (Displacement = average velocity x time). These equations are essential for solving problems related to linear motion.

Lesson Outline

<ul> <li>Linear Motion Introduction <ul> <li>Linear motion occurs when an object's acceleration and velocity are in one-dimension, that means just horizontal motion, just vertical motion, or just motion along a diagonal line.</li> <li>Once you start combining these types of motion, it's no longer one-dimensional and therefore, no longer linear.</li> <li>We'll only be looking at linear motion with constant acceleration here.</li> <li>Acceleration is caused by unbalanced forces.</li> </ul> </li> <li>Opposed Forces <ul> <li>When at rest on a surface, downward gravitational force is equal to the upward normal force.</li> </ul> </li> <li>Free Fall <ul> <li>Gravity is the only force acting on an object during free fall.</li> <li>Acceleration due to gravity on Earth is approximated to be -10 m/s² (actual value ~-9.81 m/s²), which is considered to be negative because the downward force is conventionally interpreted as a negative direction.</li> <li>Terminal velocity is when air resistance equals an object's weight, causing it to stop accelerating and maintain a constant velocity.</li> </ul> </li> <li>Four Kinematic Equations <ul> <li>vf = vi + a*t (Velocity = initial velocity + acceleration x time)</li> <li>d = vi*t + 0.5*a*t^2 (Displacement = initial velocity x time + acceleration x time squared / 2)</li> <li>vf^2 = vi^2 + 2*a*x (Velocity squared = initial velocity squared + 2 x acceleration x displacement)</li> <li>x = 0.5*(vi + vf)*t (Displacement = average velocity x time)</li> </ul> </li> </ul>

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FAQs

What is the relationship between linear motion, unbalanced forces, and constant acceleration?

Linear motion, or one-dimensional motion, occurs when an object is moving in a straight line. Unbalanced forces come into play when the net force acting on the object is not zero, causing the object to accelerate. Constant acceleration occurs when the object's velocity changes by a consistent amount over time, which is directly related to unbalanced forces acting on the object in linear motion.

How do the kinematic equations describe linear motion under constant acceleration?

The kinematic equations are a set of four equations used to describe the motion of an object experiencing constant acceleration in one-dimensional motion. These equations relate displacement, initial velocity, final velocity, acceleration, and time, allowing us to predict an object's position, motion, and other parameters at any given point in time. The kinematic equations are as follows: vf = vi + a*t, d = vi*t + 0.5*a*t^2, vf^2 = vi^2 + 2*a*d, and d = 0.5*(vi + vf)*t.

What factors determine the terminal velocity of an object in free fall?

Terminal velocity is the constant speed reached by an object when the force of gravity pulling it down is balanced by the drag force acting on it in the opposite direction. The terminal velocity depends on the object's mass, the acceleration due to gravity, the drag coefficient (which is influenced by the object's shape and surface area), and the density of the fluid medium (usually air) through which the object is falling. In short, terminal velocity is determined by the balance between gravitational and aerodynamic forces.

How does acceleration due to gravity affect objects in free fall?

Acceleration due to gravity is the constant acceleration experienced by an object in free fall, which is the result of the Earth's gravitational pull. On Earth, this value is approximately 9.81 meters per second squared (m/s²) downward. For objects in free fall, this acceleration causes their velocity to increase in the downward direction. The acceleration due to gravity not only influences the motion of objects in free fall but also provides a basis for the study of projectile motion and other gravity-related phenomena.