Mr. Conkey Physical Science Ch. 11 Motion Mr. Conkey Physical Science Ch. 11

Distance and Displacement Choosing a frame of reference To describe motion accurately and completely, a frame of reference is needed Frame of reference – a system of objects that are not moving with respect to one another

How fast are you moving? Relative motion – movement in relation to a frame of reference Which frame to choose? Depends on what you are measuring.

Measuring Distance Distance – the length of a path between two points length of path from the starting point to the ending point SI unit for measuring distance = meter (m) Large distance = (km); shorter = (cm)

Measuring Displacements Displacement – the direction from the starting point and the length of a straight line from the starting point to the ending point Displacement is an example of a vector

Combining Displacements Vector – a quantity that has magnitude and direction Magnitude can be amount, length, or size Add displacements using vector addition (the combining of vector magnitudes and directions)

Combining Displacements (cont.) When combining displacement vectors along a straight line, vectors can be added or subtracted Figure A shows vector addition, figure B shows vector subtraction.

Displacement Not Along a Straight Path Resultant vector – the vector sum of two or more vectors What is the resultant vector for the image to the right? Formula for the hypotenuse of a right triangle = a² + b² = c² ; rearranged it is c = 𝑎 2 + 𝑏 2 So, 1600 +900 = 50 𝑚

Try this example A child walks from her home to school travelling north and east. What is the total distance the child walked? What is the total displacement in blocks?

Speed and Velocity Speed – the ratio of the distance an object moves to the amount of time the object moves SI unit for speed is meters per second Average speed – measured for the entire duration of the trip Instantaneous speed – measured at a particular instant As with distance, speed measurement is relative to what you are talking about; meters per second versus kilometers per hour

Average Speed Average speed = Total distance Speed Variations Total time Speed Variations

Sample Problem You took a family vacation and travelled 35 kilometers in 0.4 hours, and then another 53 kilometers in 0.6 hours. What is your average speed?

Instantaneous Speed Instantaneous speed – the rate at which an object is moving at a given moment in time Graphing motion The slope of a line on a distance – time graph is speed

Velocity Velocity – The speed and direction of a moving object Velocity is a vector Two or more velocities add by vector addition

Acceleration Acceleration – changes in speed, direction, or both (velocity) Acceleration is a vector Changes in speed – positive acceleration (increasing) or negative acceleration (decreasing aka deceleration) Example of acceleration: free fall

Acceleration (cont.) Changes in direction – acceleration can change even if speed is constant (e.g. a carousel) Constant acceleration – a steady change in velocity

Calculating Acceleration Acceleration can be calculated for straight-line motion by dividing the change in velocity by the total time Acceleration formula – a is the acceleration (unknown), vi is the initial velocity, vf is the final velocity, and t is the total time

Sample Problem A ball rolls down a ramp, starting from rest. After two seconds, its velocity is 6 meters per second. What is the acceleration of the ball? Using the formula, a = (6 m/s - 0 m/s) / 2 s ; answer is a = 3 m/s² down the ramp.

Ball and Ramp activity Now lets first calculate the average speed of the marble as it rolls down each of the ramps (sketch the marble and ramp and record each of these average speeds into your notes) Finally, lets calculate the acceleration of the ball down each of the ramps (again record these into your notes). Discuss the differences between each ramp(if any) and why you think this is happening.

Graphs of Acceleration The slope of a speed-time graph is acceleration Linear graph – a graph where the displayed data form straight line parts.

Distance-Time Graphs Nonlinear graph – a curve connects the data points that are plotted Instantaneous acceleration – how fast a velocity is changing at a specific instant

This is the end of chapter 11!!! (wow, that was fast, get it?)