Motion

Motion - Beware of moving objects In the study of motions objects will be moving. Terms –A) Distance vs. Displacement –B) Speed vs. Velocity –C) Acceleration –D) Acceleration due to Gravity

Measurements All measurements must include a unit! Without a unit the answer is incomplete. For example:

A) Distance vs. Displacement Distance - measures the total amount of area covered. If we start at point A and end at point A the distance traveled is found: 4m 8m Add up all the legs of the journey: 4m + 8m + 4m + 8m = 24m A

A) Distance vs. Displacement Displacement is another word for position. For position the only important value is how far apart are the starting and ending point! 4m 8m A To calculate displacement: 1. Observe the starting and ending points. 2. Calculate the distance between the two.

A) Distance vs. Displacement In this example the start and end point are the same. The total displacement is then 0m. 4m 8m A

A) Distance vs. Displacement Calculate the Distance and Displacement of the following: 500m StartEnd Start/ End

B) Speed vs. Velocity Speed is a measure of how quickly distance is covered. Words “How quick” = time. Speed = Distance/Time –Measured in m/s –Scalar Measure –Positive speed --> going faster –Negative speed --> slowing down

B) Speed vs. Velocity Velocity measures how quickly the position of an object changes. –Velocity = Displacement/Time –Velocity is a vector –Unit is m/s v = s/t

B) Speed vs. Velocity A car travels 400m in 20sec. What is its speed? –v = s/t –v = 400m/20sec –v = 20m/s A student has a speed of 10m/s for 6 seconds. How far does the student travel? v = s/t 10m/s = s/6sec s = (10m/s)(6sec) s = 60m

C) Acceleration Acceleration measures the rate at which an object changes velocity. To calculate acceleration 2 measures of velocity must be known: starting and ending. The period of time must also be measured.

C)Acceleration An object accelerates (changes its velocity) in a couple of ways. –Increases velocity –Decreases velocity –Changes direction When an object DOES NOT change velocity/direction it is not accelerating.

C) Acceleration

Acceleration is abbreviated with the symbol a. It is a vector measurement. Compares changes in velocity over a period of time. The unit is m/s 2 a = (v f -v i )/∆t

C) Acceleration The bowling ball in my hands is at rest. When I throw it at you it hits your head with a final velocity of 12m/s. The ball takes 3 seconds to hit you. What is the ball’s acceleration? a = (v f -v i )/∆t v i = 0m/s v f = 12m/s t = 3s a = (12m/s-0m/s)/3s a = (12m/s)/3s a = 4m/s 2

C) Acceleration A student is walking at 2m/s. Something shiny flies by and the student takes off reaching a final velocity of 6m/s. It takes her 4s to reach this velocity. What is her acceleration? a = (vf-vi)/∆t a = (6m/s-2m/s)/4s a = (4m/s)/4s a = 1m/s 2

D) Acceleration Due to Gravity Gravity is a force felt on all objects. It pulls objects towards one another. The earth’s gravity pulls everything towards the center, we feel this as a downward pull. The rate at which objects are pulled towards the earth is the same.

D) Acceleration Due to Gravity All objects are pulled at the same rate. Therefore, acceleration downwards for all objects is the same. Acceleration due to gravity is a set value of 9.8m/s 2 g = 9.8m/s 2

D) Acceleration Due to Gravity A student is thrown from the top of Prep. The student is at rest on the roof. The flight is 4s long. With what velocity do they hit the ground? a = (v f -v i )/∆t 9.8m/s 2 = (v f -0m/s)/4s 9.8m/s 2 = (v f )/4s 39.2m/s = v f