Scientific Notation Scientific notation takes the form: M x 10 n M is some number between 1 and 9 n represents the number of decimal places to be moved – A positive n indicates that the number is large – A negative n indicates that the number is between 0 and 1

Converting to Scientific Notation Move the decimal so that there is one number between 1-9 in front of the decimal. – If there is no decimal, it is located after the last 0 at the right side of the number. – If you move the decimal to the left the exponent is positive and if you move the decimal to the right the exponent is negative. Example 1: = Example 2: =

Convert the following to scientific notation = = = = Convert the following to standard notation 8.23 x 10 3 = 7.12 x = 3.67 x 10 8 = x =

Significant Figures Measured quantities are always reported in a way that shows the precision of the measurement. – Precision is the degree of exactness of a measurement, how many decimal places an instrument can measure. Significant figures are digits in a measurement that are known with certainty. Accuracy is the extent at which a measurement approaches the true value.

Degree of Precision

Draw darts to show the following Good accuracy and good precision Good accuracy and poor precision Poor accuracy and good precision Poor accuracy and poor precision

Significant Figures If the decimal is present start from the left side and start counting digits when you see a number from 1-9. If the decimal is absent start form the right side and start counting digits when you see a number from 1-9. Example 1: = Example 2: = Pacific Side Decimal is present Atlantic Side Decimal is absent

Write the number of significant figures = x 10 4 = = 0.1 x =

Calculations using significant figures When multiplying or dividing, round to the least number of significant figures in any of the factors. Example: 23.0cm x 432 cm x 19cm = 190,000cm 3 When adding or subtracting, round your answer to the least number of decimal places in any of the numbers that makes up your answer. Example: ml ml ml = 255.5ml

Perform the following calculations expressing the answer in the correct number of significant figures m x1.2 m = 3.5 cm x 2.50 cm x cm = cm 3  3.2 cm = m/s m/s = 150 ml – 23.5 ml =

International System of Units Based on metric system Common units and quantities – Length – Volume – Mass – Temperature – Energy

Conversions Move the decimal point to the left or right to convert within the metric system. – If you are going from a smaller unit to a larger unit move the decimal to the left. – If you are going from a larger unit to a smaller unit move the decimal to the right. kilohectodeca Base Unit (1) decicentimilli khdaMeter (m)dcm Gram (g) Liter (l)

Convert the following measurements 245 m = _____________ cm 305 kg = _____________ g 35 mm = ______________ m 1250 cm = _____________ m 358 ml = ______________ l 2350 g = ______________kg 35 dm = ______________m 67 hm = ______________m

In order to convert between different units of measurement you need to use conversion factors and the factor-label method. Example: A football field is 100. yds long. How long is that in m? 100. yards = 91.7 m 1.09 yd 1 m

Example: A horse can gallop at a speed of 42.0 mph. How fast can the horse gallop in m/s? h 42.0 mi = 18.8 m/s 3600 s 1 h 1 mi 1609 m

Convert the following English Standard Units to Metric Units. If I were to hit a home run down the left side of Jacobs Field the ball would have to travel at least 325 ft. How far is that in m? The top speed of a human is 10.4 m/s. How fast is that in mph?

Convert the following English Standard Units to Metric Units. A race car can travel around 225 mph. How fast is that in m/s? A person can walk about 3.1 mph. How fast is that in m/s?

Motion How can you tell an object is moving? – An object must change position with respect to a stationary background called a reference. What is relative motion?relative motion – It is movement in relation to a frame or reference.

Distance vs. Displacement Distance is the length of the path between two points Displacement includes direction How is displacement different from Distance? What is the displacement of a roller coaster after one complete trip around the track?

Speed What is the difference between average speed and instantaneous speed? – Average speed is the total distance divided by the total time – Instantaneous is the rate at a given moment

Calculating Speed What units do you measure speed in? – We measure the speed of our cars and highway speed limits in miles/hour. – However in science class we measure speed using the SI units of meters/second. – Most other countries have highway speed limits posted in kilometers/hour, which is also a metric unit.

Calculating Speed Speed or velocity = distance/time

Example Problem A car traveled 350 miles toward New York City for 5 hours. What was the velocity of the car in mph and m/s?

Example Problem A car traveled 35 miles/hour for 4 hours toward Chicago. How far did the car travel in miles and meters?

Example Problem A plane travels 1925 miles toward Colorado at a velocity of 550 miles/hour. How much time has the plane been traveling in hours and seconds?

Graphing Motion The slope on a distance-time graph is speed The slope on a velocity-time graph is acceleration

Distance-Time Graph

Speed vs. Velocity What’s the difference between speed and velocity? – The speed describes how fast an object is moving. – Velocity is a speed in a given direction.

Acceleration What happens to you when you slam on the brakes in a car? What happens if you speed up very fast like on the top-thrill dragster at Cedar Point? Acceleration is defined as a change in velocity or direction divided by the time interval in which the change occurred.

Calculating Acceleration

Example Problem The Top Thrill Dragster at Cedar Point goes from 0 m/s to 53.6 m/s (120 mph) in 4 seconds. What is its acceleration?

Example Problem A car traveling home at a velocity of 15.6 m/s slams on its brakes and comes to a stop to avoid a dog. If it takes 5 seconds to stop, what is the cars acceleration?

Example Problem A Porsche Boxster has an acceleration of 4.51 m/s 2. If the car starts from rest how much time would it take for the vehicle to reach a speed of 11.3 m/s?

Example Problem A bicyclist starts from rest and accelerates at 0.89 m/s 2 during a 5.0 s interval. What is the change in speed of the bicyclist and bicycle?

Example Problem A golf ball thrown from the top of the sears tower accelerates at 9.8 m/s 2 toward the ground and lands on the pavement 9.2 seconds. If the ball’s final speed is 93.0 m/s what was the speed with which the ball was initial thrown?