Introduction to Kinematics Unit 1 Presentation 3

What is Kinematics? Kinematics: The study of motion without regard to its cause Constant or Zero Acceleration Kinematic motion can be described by six basic equations

Six Basic Kinematic Equations

Some Definitions Scalar: Magnitude Only (No direction) Vector: Magnitude + Direction Everything in Physics is either a Scalar or a Vector Never both and never neither!

Distance vs. Displacement Distance is a scalar Total distance covered, no regard to direction Displacement is a vector Change in position, WITH regards to direction. Always a linear, one-directional change.

Distance vs. Displacement Lets say Mr. Hamm walks from the Initial Position to the Final Position along the blue arrows. That is his PATH, and the distance covered is the total length of the two arrows. Final Position The displacement of Mr. Hamm is represented by the red arrow, and is equal to the length of that one arrow and the direction of the arrow (represented by a bearing). Displacement is always less than or equal to distance. Initial Position

Speed vs. Velocity Speed is a scalar Velocity is a vector Speed: change in distance divided by the change in time Velocity is a vector Velocity: change in displacement divided by the change in time. Velocity has a magnitude and a direction.

Speed and Velocity Average velocity is NOT the same as average speed. If you run from x=0 m to x=25 m and then back again to x=0 m in 5 seconds, your average velocity is zero (displacement is zero), which your average speed is 10 m/s.

Average vs. Instantaneous Velocity can be found by calculating the slope on a displacement vs. time graph. Velocity AT a specific time (ti in this case) Average Velocity: Slope of Secant Line Average velocity over a certain time interval (to to tf) to ti tf

Acceleration Acceleration is always a vector Acceleration can be average (over a time interval) or instantaneous (at a specific time)

Meter per second squared (m/s2) SI Units Measurement SI Unit Distance Meter (m) Displacement Speed Meter per second (m/s) Velocity Acceleration Meter per second squared (m/s2) Time Second

Graph Analysis Example A particle moves along the x-axis according to the graph on the left. What is the average velocity of the particle in the time interval 1 < t < 5 seconds? To find the average velocity, we must find the slope of the line in this interval. Slope = Hence, the average velocity over this time interval is 1 m/s.

Displacement Can we have negative displacement? YES!!! For example, the particle in the last example moves from position x=0 m to x=-4 m (moves to the left instead of the right). The negative sign represents the “negative” direction of the displacement. The magnitude of the motion is still 4 meters, just in the “negative” direction. Remember, vectors are magnitude AND direction! See the next example.

Another Graph Analysis Example A particle moves along the x-axis according to the graph on the left. What is the average velocity of the particle in the time interval 6 < t < 8 seconds? To find the average velocity, we must find the slope of the line in this interval. Slope = Hence, the velocity is -4 m/s. Since this value is negative, the particle must be moving to the LEFT, or along the negative x-axis, which is true.

Another Graph Example A particle moves along the x-axis with a velocity according to the graph on the left. What is the average acceleration of the particle in the time interval 1 < t < 4 seconds? To find the average velocity, we must find the slope of the line in this interval. Slope = Hence, the average acceleration over this time interval is 2 m/s2.