DISPLACEMENT AND VELOCITY. Chapter 2-1. Objectives. Describe motion in terms of frame of reference, displacement, time and velocity. Calculate displacement, velocity and time interval. Interpret position vs. time graphs.
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Objectives • Describe motion in terms of frame of reference, displacement, time and velocity. • Calculate displacement, velocity and time interval. • Interpret position vs. time graphs.
Kinematics deals with the concepts that are needed to describe motion. • Dynamics deals with the effect that force shave on motion. • Together, kinematics and dynamics form the branch of physics known as Mechanics.
2.1 Displacement • As any object moves from one position to another, the length of the straight line drawn from its initial position to the object’s final position is called displacement. • Displacement is the change in position of an object. • Displacement doesn’t always tell you distance an object moved. • Displacement = final position – initial position • ∆x = xf-xo • Si units – meters (m)
2.1 Displacement • Displacement is not always equal to the distance traveled. • Displacement can be positive or negative. • If displacement is positive, the object moves to the right. • If the displacement is negative, the object moves to the left.
2.2 Speed and Velocity Average speed is the distance traveled divided by the time required to cover the distance. SI units for speed: meters per second (m/s)
2.2 Speed and Velocity Average velocity is the displacement divided by the elapsed time. SI units for velocity: meters per second (m/s)
2.2 Speed and Velocity • Velocity gives both direction and magnitude (amount) while speed only gives the magnitude - no direction • Average velocity does not tell you the speed or velocity of the moving object at each moment. • Average velocity can be positive or negative depending on direction moved. • Time can never be negative!
Average Velocity: • The slope of a position vs. time graph is called the average velocity.
Speed and velocity: • Velocity and speed can be used interchangeably in everyday language • In Physics, however, there is a distinction: • Speed is a Scalar quantity (numerical value = magnitude only) • Velocity is Vector quantity - Describes motion with both direction and a numerical value (magnitude and direction)
Constant Velocity Model: Velocity vs. Time Graph • With constant velocity, • On a graph of velocity vs. time, displacement can be calculated by finding the area under the graph. • If the velocity is negative, the displacement calculate will be negative.
More practice:- ‘GUESS’ method • A vehicle travels 2345 m in 315 s toward the evening sun. What is its velocity? • Given: Displacement = 2345 m , time = 315 s • Unknown: Velocity = ? • Equation and model: v = D/t (kinematics) • Separate the unknown: ----- • Substitute and solve: V = 2345 / 315 • 7.44 m/s • does the answer make sense? • Yes!!
Displacement for constant acceleration • The displacement from time 0 to time t is the area under the velocity graph from 0 to t. • Area = ½ b h v (m/s) t (s)
Instantaneous Velocity The instantaneous velocity indicates how fast the car moves and the direction of motion at each instant of time.
2.3 Acceleration • The notion of acceleration emerges when a change in velocity is combined with the time during which the change occurs. • Accelerationis the measure of how fast something speeds up or slows down
2.3 Acceleration DEFINITION OF AVERAGE ACCELERATION SI units for acceleration: (m/s2)
Changes in velocity: • Instantaneous acceleration: • Since in some situations, the acceleration of an object can be constant , as a result, it will be the same value at any instant of time. • The plus or minus sign before the number indicates the two possible directions for the acceleration vector when the motion is along a straight line.
Interpret The Graph Below:Distance vs. Time In the first part of the graph the object is moving with constant velocity. In the second part of the graph the object is at rest (not moving). In the third part the object is again moving with constant velocity.
Interpret The Graph Below:Velocity vs. Time (constant acceleration - negative) The objects velocity is decreasing as time passes – it is decelerating / slowing down The straight line shows that it is constant deceleration.
2.4 Equations of Kinematics for Constant Acceleration For one dimensional motion it is customary to dispense with the use of boldface symbols overdrawn with arrows for the displacement, velocity, and acceleration vectors. We will, however, continue to convey the directions with a plus or minus sign.
Free Fall acceleration: • An object thrown or dropped in the presence of Earth’s gravity experiences a constant acceleration directed toward the center of the earth. • This acceleration is called the free- fall acceleration, or the acceleration due to gravity. • Free fall acceleration is the same for all objects, regardless of their mass.
Free fall acceleration: • The value for free fall acceleration used in this book is: • g = 9.81 m/s2. • In this book, the direction of the free fall acceleration is considered to be negative because the object accelerates toward earth. Positive Negative
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