Kinematics 1D

Kinematics

a subfield of physics and a branch of geometry, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move.

Geometry

a branch of mathematics concerned with the properties of space such as distance, shape, size, and the relative position of figures.

Scalars

Scalars are magnitude only, like distance; for example, she walked 56 metres.

vectors

vectors are quantities with magnitude and direction, like displacement; for example, she walked 56 metres east. Vector quantities have a little arrow pointing to the right on top of their symbol. Since it is a vector, that means that there are two ways that it can change: change in magnitude and change in direction.

Distance

Distance $\mathrm{d}$ is the total length of the path travelled;

displacement

displacement $\overrightarrow{d}$ is the change in an object’s position. Displacements can be either positive or negative depending on the object’s direction of motion from the starting point

Instantaneous speed / velocity

The speed is calculated for a time interval which is very small. Instantaneous speed is a scalar. Instantaneous velocity is the velocity calculated for a time interval which is very small. Instantaneous velocity is a vector.

uniform motion

In uniform motion, speed is constant, and velocity is constant as well. In this scenario, the object travels equal distances in equal intervals of time, resulting in no acceleration.

Acceleration

The rate of change of velocity with respect to time. Units of acceleration = m/s2.

Acceleration Due to Gravity

A freely falling object will experience acceleration due to gravity. Near the earth’s surface, the acceleration due to gravity is g =9.81 m/s2 down

Acceleration and slopes

Acceleration is the slope of a velocity vs. time graph. The concept of ‘slope’ is typically applied to a straight line (e.g. a linear function). We can calculate the slope of a tangent line. A tangent line touches the curve at only one point.