Acceleration and Average Speed

Acceleration and Average Speed Acceleration Acceleration 2 (in meter/sec ) Acceleration is how fast you change speed OR how much the speed changed in a certain amount of time. Change of Speed (in meters/sec) ΔV a = ΔT Change of Time (in seconds) T Speed equal change of distance divided by change of time. ΔV = Vf - Vi Example: Calculate Acceleration ΔT=T2-T1 a = ΔS/ΔT, not a = S/T. Why? If a car is traveling at 60 m/s for 20 sec, S = 60 m/s, but ΔS = 0 m/s. No change of speed: no acceleration. Ex. A plane starts at rest and ends up going 200 m/s in 10 secs. Calculate acceleration. Step 1: Variables Step 2: Find ΔS Step 3: Formula ΔS=S2 - S1 S1 = 0 m/s (“starts at rest”) S2 = 200 m/s ΔT = 10 seconds a=? a = ΔS/ΔT = 200 - 0 = 200 m/s Step 2: Find ΔS Step 3: Formula ΔS=S2-S1 = 0 - 400 = -400 m/s NOTICE NEGATIVE ΔS a = ΔS/ΔT Step 1: Variables S1 = 400 m/s S2 = 0 m/s (“then stops”) ΔT = 20 seconds a=? a = (200 m/s)/(10 s) = 20 m/s 2 Deceleration means an object is slowing down and has a negative sign. Ex. A race car starts at 400 m/s and then stops in 20 seconds. Calculate the car’s acceleration. Example: Calculate Deceleration Step 4: Solve Step 4: Solve a = (-400 m/s)/(20 s) = -20 m/s 2 Negative sign means deceleration. Speed vs. Velocity S Average Speed ave =D total Speed is a Scalar Velocity is a Vector /T total Ex. A person walks 4 miles in 2 hours, then stops for an hour for lunch. After lunch they walk 8 miles in 3 hours. Calculate the person’s average speed. Distance Careful—distance is 0 miles because “stops ... for lunch”. TOTALS: Savg = Time 4 miles 0 miles 2 hours 1 hour 8 miles 3 hours 12 miles 6 hours Dtotal / Ttotal = 12 mi/6 hr = 2mph Speed has no direction; Scalars have no direction. Velocity has direction; Vectors have direction. A person walks 4 m/s—speed (no direction). A person walks 2 m/s north— velocity (direction is given). A car drives 60 mph toward Dallas—velocity. A car drives 30 mph—speed. o A 14 newton force pull 30 left of north—vector. A boat is pulled by a 53 newton force—scalar. Vectors have magnitude and direction. Velocity is a vector with magnitude and direction. Speed (S) or Velocity (V) V A bike goes 25 m/s toward main street. S A person walks 4 mph. S A plane flies 200 m/s. speed vs. time graphs; Match the variables with quantities. Scalar (S) or Vector (V) V V_ A bird flies 100 mph due south. 40 mph toward Dallas. 1. a = 3 m/s2 2. S or v = 23 meters/sec S____ A 25 N force pulls on a wagon. V S 3. m = 23 kilograms 4. D = 23 meters 10 meters up the hill. 5. F = 23 newtons 12 meter per sec2. 6. T = 23 sec A person starts running from 2 m/s to 6 m/s in 2 seconds. Calculate the person’s acceleration. Variables: S1=2 m/s Solve: 6 m/s – 2 m/s= 4 m/s S2=6 m/s 4m/s / 2 sec = 2 m/s2 T= 2 seconds A=? A plane stops from 250 mph in 25 seconds. Calculate the planes acceleration. Variables: S1= 250 mph S2= 0 mph T=25 seconds Formula: a = ΔS/ΔT Solve: 0 mph – 250 mph= -250mph 250 mph/ 25 seconds= -10m/s2 Formula: a = ΔS/ΔT A dragster’s top acceleration is 60 m/s2. If it accelerates for 3 seconds from the starting line, how fast will it be going? A guy bikes 15 miles in 1 hour, then rests for an hour. Then he bikes 25 in 2 hours. What was his average speed for the trip? Variables: Total time = 4 hours 15 miles 0 miles 25 miles Variables: a= 60m/s2 T= 3 seconds Solve: 15 miles/1-hour= 15 mi/hour 0 miles/ 1 hour= 0 25 miles/2 hour= 12.5 mi/hour with rest included= 9.5 miles/hour no rest included= 13.75 miles/hour Formula: a = ΔS/ΔT Solve: 0+60 * 3= 180 m/s Formula: v = u + at Speed vs. Time Which graph segments fit the following: A 70 60 50 40 30 20 10 0 Speed Speed (m/s) Speed vs . Time Constant speed: A,C B C D Deceleration: B Accelerating: D Time 0 2 4 6 8 Time (s e c) Find the acceleration for the above graph:4.16 m/s2 10 12 The slope of a position vs. time graph means: Velocity The slope of a speed vs. time graph means: Acceleration