Linear Kinematics

Motion in a Straight Line When learning about linear kinematice you first have to understand that motion is relative, this means:

Motion is relative An object can be moving with respect to one body and at the same time be at rest or be moving at a different speed with respect to a second body

Frame of Reference A frame of reference is a set of axes used to describe the position and motion of a body

Speed vs. Velocity The speed of a body tells us how far it travels during every unit of time that it maintains that speed. Velocity is a vector, it tells us two things about a moving body; it’s speed and direction of motion.

Uniform and Accelerated Motion In uniform motion both the speed and direction of the moving body remain the same. Motion with a changing velocity is accelerated motion

Acceleration The acceleration of a body is the rate at which the speed is changing You can find acceleration of a body by dividing the change that takes place in it’s speed by the time during which the change occured. Example:

Example of Acceleration The speed of an airplane increases steadily the first 5secs of take off from 0 to 10 m/s. The change in it’s speed is then 10-0=10m/s, it’s acceleration is therefore 10/5=2m/s/s

Average speed and Instantaneous speed Average Speed is found by dividing the distance traveled by the travel time To find the distance multiply average speed and time In the case of a body that moves at a constant speed in a straight line, the instantaneous speed and the average speed are equal at all times d = vt

Freely Falling Bodies A body falling freely in a vacuum is a very important example of motion at a constant acceleration. Galileo showed that a body speeds up as it falls with an acceleration of 9.8 m/s 9.8m/s is the acceleration of gravity, it is represented as the letter g. g=9.8m/s

Some equations to know a=v-vo v=vo+at Average velocity=vo+v/2 d=vot+1/2a(time squared) d=vt

Graphical Analysis of Motion The slope of a distance - time graph represents the speed In a speed - time graph the area between the speed-time line and the horizontal axis represents the distance traveled by the body up to that time.

Graphical Analysis of Motion cont. The slope of the tangent to the distance-time graph at any point (P) is the instantaneous speed at that point In a speed-time graph the slope of the speed -time line gives the acceleration of the body at each point

Galileo’s Analysis The law in Galileo’s day saidthat objects do not fall in air with the same acceleration (ex: feather and brick), the heavier the object the faster it falls. Galileo suggested that the true law was obscured by the fact that the friction of the air changes the rate of fall of different bodies in different ways

Galileo cont. Galileo then reasoned that in a vacuum, any two bodies made of the same material will fall at the same rate regardless of their weight