4.1 Speed The aim of this lesson is to be able to use the correct formulas to calculate speed, distance or time Speed is the distance traveled per unit of time. Speed (s) = distance (d) time (t) Each variable measured by units: Distance: meters (m), miles (mi) Time:seconds (s), hours (hr), minutes (min) Speed: meters per second (m/s), miles per hour (mi/hr), kilometers per hour (km/hr) 3 2 TYPES OF SPEED (Average, Constant) A . Constant Speed is when the object covers equal distances in equal amounts of time. B . Average speed is the total distance traveled divided by the total time. It can be calculated using the following formula: Average Speed is: Total distance = distance traveled speed = distance time all over Total time = final time (end) minus initial time (beginning) 4 Four Step Approach to Solving Problems G.U.E.S.S.A. Step 1 READ THE PROBLEM. Draw a picture. Step 2 IDENTIFY THE VARIABLES Write down what you know. GIVEN What are you trying to find? UNKNOWN Step 3 WRITE FORMULA EQUATION Set up the formula. (The formula should match the unknown.) Step 4 PLUG IN THE NUMBERS. SUBSTITUTE DO THE MATH SOLVE. Check ANSWER with UNITS 5 The 3 formulas for Speed, Time & Distance: Distance Speed = Time Solving for Speed Distance Time = Distance = Speed x Time Speed Solving for Time Solving for Distance D Remember them from this triangle: S T Reminder: How to change minutes to hours 15 mins÷ 60 = 0•25 hour So: 3 hours 15 mins = 3•25 hours 30 mins ÷ 60 = 0•5 hour So: 7 hours 30 mins = 7•5 hours 45 mins÷ 60 = 0•75 hour So: 2 hours 45 mins = 2•75 hours “A car traveled 110 km in 2 hours.” calculate the speed Step 1 Read the problem. Draw a picture. 110 km 2 hours d= t= s= Formula Plug-in Units, units, units! Answer 8 “A car traveled 110 km in 2 hours.” Step 2 Write down what you know. GIVEN What are you trying to find? UNKNOWN 110 km 2 hours d = 110 km t = 2 hours s= Formula Plug-in Units, units, units! Answer 9 “A car traveled 110 km in 2 hours.” Step 3 Set up the formula. FORMULA SHOULD MATCH THE UNKNOWN s= d = 110 km t = 2 hours s= Formula d t Plug-in Units, units, units! Answer 10 “A car traveled 110 km in 2 hours.” Step 3 d = 110 km t = 2 hours s= Formula S= Set up the formula. EQUATION Plug-in Answer d t Units, units, units! 11 “A car traveled 110 km in 2 hours.” Step 4 Plug-in the numbers. SUBSTITUTE AND SOLVE. CHECK UNITS 55 km/hr Formula d = 110 km d t = 2 hours S= s = 55 km/hr t Plug-in Answer S = 110 km S = 55 km/hr 2 hr Units, units, units! 12 A windsurfer travelled 28 km in 1 hour 45 mins. Calculate his speed. Speed = = Distance Time D S T 28 1•75 1 hour 45 mins = 16 km/h Answer: His speed was 16 km / hour A salesman travelled at an average speed of 50 km/h for 2 hours 30 mins. How far did he travel? D Distance = Speed x Time S = 50 x 2•5 T 2 hour 30 mins = 125 km Answer: He travelled 125 km A train travelled 555 km at an average speed of 60 km/hr. How long did the journey take? Distance Time = Speed = 555 60 = 9•25 hours D S T = 9 hours 15 mins Answer: It took 9 hours 15 minutes Practice If a runner runs 100 meters in 50 seconds, what is his speed in meters per second? How far could this runner run in 25 seconds? Speed A rocket is traveling at 10 m/s. How long does it take the rocket to travel 30 m? Speed A racecar is traveling at 85.0 m/s. How far does the car travel in 30.0 s? and Average speed distance traveled over (Total total time) Both do not involve direction. 19 Average Speed A car drives 100 meters in 5 seconds. 1s 2 3 4 5 100 m What is the car’s average speed? s = d/t s = (100 m) / (5 s) = 20 m/s Average speed Average speed What is the difference between speed and velocity? Velocity has speed & direction. 55 mi/hr All of these cars had different velocities because they were traveling in different directions. 23