Summary Intro to motion / Kinematics / Forces & Newton’s Laws

Complete Description: Kinematics is the branch of physics that focuses on describing motion without considering the forces that cause it. It answers questions about how objects move, how fast they move, and how their motion changes over time. A scalar quantity describes magnitude only. Examples include distance, speed, and time. Scalars do not include direction and are always positive. A vector quantity includes both magnitude and direction, making it more specific. Examples of vectors include displacement, velocity, and acceleration. Direction is essential for vectors because motion can occur in more than one orientation. Distance is the total length of the path an object travels, regardless of direction. It depends entirely on the path taken and always increases as motion continues. Distance is a scalar quantity. Displacement, on the other hand, is the change in position from the starting point to the ending point. It is calculated as final position minus initial position. Displacement is a vector because it includes direction and can be positive, negative, or zero. For example, in the football scenario, the player travels a total distance of 130 yards, but because some of the motion occurs backward, the overall displacement is only 80 yards downfield. When motion occurs in two dimensions, displacement must be found using vector addition. The straight-line distance between the starting and ending points represents the true displacement, which in this case is approximately 17.5 meters. Motion graphs visually represent how objects move. On a position-time graph, the slope represents velocity. A steeper slope means faster motion, while a horizontal line indicates the object is at rest. On a velocity-time graph, the slope represents acceleration, showing how velocity changes over time. The area under a velocity-time graph represents displacement because it combines speed and time. Similarly, the area under an acceleration-time graph represents the change in velocity. When acceleration is zero between two and three seconds, velocity remains constant during that interval. Over the entire time span from zero to seven seconds, the total displacement is five meters. Kinematic equations allow motion to be predicted mathematically when acceleration is constant. These equations rely on standard variables such as position measured in meters, velocity measured in meters per second, acceleration measured in meters per second squared, and time measured in seconds. Correct units are essential for accurate calculations. In vertical motion near Earth’s surface, acceleration due to gravity is constant at −9.8 meters per second squared. The negative sign indicates that gravity acts downward. At the maximum height of a projectile, the vertical velocity becomes zero because gravity has slowed the object before reversing its direction. Gravity continues acting at all times, even at the highest point. In ideal projectile motion, horizontal acceleration is zero. This means horizontal velocity remains constant throughout the motion. Vertical and horizontal motions are independent and are only connected through time. Using kinematic equations, the maximum height of a projectile is approximately 3.3 meters. A separate motion problem results in a total time of about 16.7 seconds. For the projectile example, the time of flight is approximately 2.02 seconds, and the horizontal range is about 20.2 meters. Forces explain why motion changes. Inertia is an object’s resistance to changes in motion and depends on mass. Objects naturally continue doing whatever they are already doing unless acted upon by a net force. Newton’s Second Law states that acceleration occurs when a net force acts on an object. This relationship is described by the equation net force equals mass times acceleration. If the net force is zero, the object does not accelerate, even if it is moving. The gravitational force acting on an object is equal to its mass multiplied by gravitational acceleration. The normal force is a contact force exerted by a surface, acting perpendicular to that surface. It adjusts to balance other forces when the object is not accelerating vertically. When forces are unbalanced, acceleration occurs. In one example, the net force produces an acceleration of 4.0 meters per second squared to the right, indicating both magnitude and direction. In the iPad problem, forces act in both horizontal and vertical directions, producing a net horizontal acceleration of approximately −0.89 meters per second squared and a vertical acceleration of about 1.15 meters per second squared. This shows the importance of breaking forces into components when analyzing motion. Friction is a force that opposes motion between surfaces in contact. In the final example, friction acts with a force of 68.6 newtons to the right, resulting in a negative acceleration of approximately −1.22 meters per second squared. This indicates that the object is slowing down. Overall, this study guide progresses from describing motion, to predicting motion, and finally to explaining motion using forces. Each unit builds on the previous one, creating a complete understanding of how objects move and why they move the way they do.