Speed and Velocity Notes

What is Speed? We see objects moving everyday. Many different kinds of motion can be described by speed. What is speed and how do we calculate it? Speed is described as the distance (change in position) an object moves over a period of time. Written as a ratio S = d/t Ex.: S = 30 m/h or S = 2 m/s

S = d/t Formula for speed Written as a ratio S = d/t Ex.: S = 30 m/h or S = 2 m/s S = d/t

Equation S = d/t S = speed d = distance t = time S = d/t

Formula for speed S = d/t S = speed d = distance t = time d S t

Rearranging formulas A. Solve for distance (d) B. Solve for time (t)

Units for Speed The SI units of speed is meters per second (m/s) Choose the appropriate units to describe speed. Ex. snowboarding at 2 m/s Driving at 65 miles/hr Running at 30 m/minute

Speed Formula Average speed is the speed calculated over the duration of a trip. Ex. Dylan snowboarded down the black diamond run at an average speed of 2.9 m/s. Calculate average speed by dividing Total distance over total time. Average Speed= Total distance/ Total time d t S

Use the GUESS method to solve word problems… Write the letters GUESS down the margins of your blank page. Write BIG– use all the space.

Underline the numbers that are GIVEN in the word problem. Circle the variable that is UNKNOWN in the word problem. (Unknown) Rearrange and write the EQUATION to solve for the unknown variable. (Equation)

SUBSTITUTE the given values into your formula. SOLVE for the appropriate variable and be sure to ***include the correct units***! (Solve)

Example Problem G: U: E: S: S: Ex. While biking down Pikes Peak, Tim traveled 10 kilometers in 0.4 hours, followed by 13 kilometers in 0.6 hrs. What was Tim’s average speed?   G: U: E: S: S: 0.4 hours 0.6 hours 13 km 10 km Average speed S = d/t S = 23/1 (10 + 13 = 23 km) (0.4 + 0.6) = 1 hour S = 23 km/hr

Example Problem G: U: E: S: S: You need to get to class, 200 meters away, and you can only walk in the hallways at about 1.5 m/s. How much time will it take to get to your class?   G: U: E: S: S: 200 m 1.5 m/s time t = d/S t = 200/1.5 t = 133.3 s

Example Problem G: U: E: S: S: If you shout into the Grand Canyon, your voice travels at the speed of sound (340 m/s) to the bottom of the canyon and back, and you hear an echo. How deep is the Grand Canyon at a spot where you can hear your echo 5.2 seconds after you shout?   G: U: E: S: S: 340 m/s 5.2 s Distance (how deep) D = S(t) d = 340*5.2 d = 1768 m

Instantaneous Speed The speed of an object at any given moment in time is instantaneous speed. Ex. Shawn the state trooper clocked Savannah riding her motorcycle at 85 m/hr. while passing the white van. The ­speedometer in your car gives you the instantaneous speed.

Distance-time Graphs ­The ­­slope ­on a distance-time graph represents speed! Ex. To find the speed between the red arrows, calculate the slope. Slope = y2-y1  8-4 = 4/2 = 2 m/s x2-x1 4-2

What is Velocity? Velocity is a vector with speed and direction. V = velocity d = distance t = time The equation for speed and velocity are the same, so the same steps to solve for speed can be applied to solve for velocity. V = d/t

What is Velocity? V = velocity d = distance t = time . d V t

Velocity is a vector! Velocity is a vector quantity, so… A change in velocity can occur when there is: a. a change in speed b. a change in direction c. or BOTH!

Answer: YES, because it is changing direction. Example Problem Ex. A sailboat may speed up or speed down depending on the wind; therefore, it’s velocity is changing. It may also change velocity by changing directions! If a sailboat is moving at a constant speed, but changing direction, is it changing in velocity too? Answer: YES, because it is changing direction.

Example Problem G: U: E: S: S: Ex. What is the velocity of a plane that traveled 3,000 miles from New York to California in 5.0 hours?   G: U: E: S: S: 3,000 miles 5 hours velocity V = d/t V = 3000/5 t = 600 mi/hr WEST Since velocity is a vector, you need direction in your answer! California is to the WEST of New York.

Combining Velocities 12 km/h east + 5 km/h east = 17 km/h east Sometimes the motion of an object involves more than one velocity. Two or more velocities add by vector addition. Example: You are canoeing down river at a velocity of 12 km/hr. The river is flowing at a velocity of 5 km/hr. What is the velocity of the canoe relative to a person standing on the riverbank watching you? 12 km/h east + 5 km/h east = 17 km/h east

Combining Velocities Example Example: A river flows at a velocity of 3 km/h east. A boat moves upstream at a velocity of 15 km/h west. What is the velocity of the boat? 15 km/h west - 3 km/h east = 12 km/h west