Introduction to Kinematics The Study of Motion Kinematics

Introduction to Kinematics: The Study of Motion

Kinematics A quantity can be described as being vector or scalar. • Vector – a quantity that is represented by both magnitude (size) & direction • Scalar - a quantity that is represented by magnitude (size) only

Kinematics Position Versus Distance • Position – the separation between an object and a reference point • Distance – the separation between two points A reference point is a designated spot from which to measure

Kinematics • Instantaneous Position – the position of an object at one instant, at one single time. • A change in position is called displacement. • d = d 2 – d 1 where d is displacement, and d 2 and d 1 are positions • Distance – scalar; Displacement – vector, and can be positive or negative

Kinematics Average Velocity – the change in position divided by the difference in time _ d d 2 – d 1 v = t t 2 – t 1 Average Velocity can also be calculated if you know an initial velocity and a final velocity… v = vf + vi 2

Kinematics Finding Displacement: d =v t Substituting in the average velocity equation: v = vf + vi d = vf + vi t 2 2 OR…. . d = ½ (vf + vi ) t

Kinematics Positive & Negative Velocities • Similar to positions and displacement, velocity can be described as being positive or negative, depending on the direction the object or body is moving. • If the direction of the body is positive, velocity is positive • Because of this, we use the terms speed for how fast an object is going & velocity for the speed and its direction

Kinematics Position-Time Graphs • A graph that shows how position depends on time • The slope is change in position (displacement) divided by time = velocity • A linear, direct relationship = constant velocity • A parabolic, direct relationship = acceleration (speeding up)

Kinematics Position – Time Graphs (cont. ) • When an object is accelerating, you can find the instantaneous velocity by using a tangent line, then calculating the slope of the tangent line

Kinematics Acceleration • Acceleration is the rate at which velocity changes • Average acceleration – the ratio of change in velocity to a change in time a = v 2 – v 1 = v t t

Kinematics • Acceleration is a vector quantity • It can be positive or negative • Positive acceleration – the velocity is increasing • Negative acceleration – the velocity is decreasing ****later, we will go further in our discussion of positive & negative accelerations…