Motion & Graphs IB PHYSICS | UNIT 2 | MOTION 2.1 Motion 2.1 Motion 2.1 Motion Learning Objectives: - Understand the difference between distance and displacement. - Understand the difference between speed and velocity. - Understand the concept of acceleration. - Analyse graphs describing motion. 2.1 Motion Mechanics: the branch of physics which concerns itself with forces, and how they affect a body’s motion. Kinematics: is the sub-branch of mechanics which studies only a body’s motion without regards to causes. Dynamics: is the sub-branch of mechanics which studies the forces which cause a body’s motion. What is Motion? An object's change in _____________ relative to a reference point. Relative to the earth: Moving 28,000 km/h Relative to the ISS: Not moving What is Motion? position An object's change in _____________ relative to a reference point. Relative to the earth: Moving 28,000 km/h Relative to the ISS: Not moving Distance vs. Displacement Distance Displacement Distance vs. Displacement Distance Total length of path followed from initial position to final position Displacement Shortest distance from an initial position to a final position Distance vs. Displacement Distance is a scalar Total length of path followed from initial position to final position Displacement is a vector *direction needs to be specified Shortest distance from an initial position to a final position βx = x2 – x1 s = x2 – x1 displacement where x2 is the final position and x1 is the initial position FYI ο· Many textbooks use βπ₯ for displacement, and IB uses π . Don’t confuse the “change in β” with the “uncertainty β” symbol. And don’t confuse π with seconds! βx = x2 – x1 s = x2 – x1 displacement where x2 is the final position and x1 is the initial position Distance = 100 + 250 = 350 m Displacement = −50 − 100 = −150 m IB Practice Question IB Practice Question Constant Displacement Distance (m) Velocity (m s-1) Not moving Time (s) Time (s) Constant Displacement Distance (m) Velocity (m s-1) Not moving Time (s) Time (s) Constant Displacement Displacement/Distance-Time graph • Stationary objects produce a horizontal (slope of zero; constant value) linear graph Velocity-Time graph • Stationary objects produce a graph with horizontal constant velocity value of zero IB Practice Question IB Practice Question Speed vs Velocity In just the same way that there are scalar and vector measures of the length of a journey, so there are two ways of measuring how quickly we cover the ground. Speed The rate of change of distance Velocity The rate of change of displacement Speed vs Velocity In just the same way that there are scalar and vector measures of the length of a journey, so there are two ways of measuring how quickly we cover the ground. Speed is a scalar The rate of change of distance Velocity is a vector *direction needs to be specified The rate of change of displacement Average Speed and Velocity πππ‘ππ π·ππ π‘ππππ Average Speed = πππ‘ππ ππππ * Always Positive πππ‘ππ π·ππ πππππππππ‘ Average Velocity = πππ‘ππ ππππ * Includes Direction v = βx / βt v=s/t velocity Consider this… The gold medalist for the men’s 400 m (one complete lap of the track) in Rio was Wayde van Niekerk with a WR time of 43.03 s. What was his average speed? Average velocity? Consider this… The gold medalist for the men’s 400 m (one complete lap of the track) in Rio was Wayde van Niekerk with a WR time of 43.03 s. What was his average speed? Average velocity? Average speed = 400 π 43.03 π Average velocity = = 9.3 π π −1 0π 43.03 π = π π π−π Consider this… The gold medalist for the men’s 400 m (one complete lap of the track) in Rio was Wayde van Niekerk with a WR time of 43.03 s. What was his average speed? Average velocity? Average speed = 400 π 43.03 π Average velocity = = 9.3 π π −1 0π 43.03 π = π π π−π *notice that the average speed is not the magnitude of the average velocity Calculating Average Speed New world record for a marathon (42.2 km) was set several years ago. Eliud Kipchoge finished in 2.03 hours. What was his average speed? Calculating Average Speed New world record for a marathon (42.2 km) was set several years ago. Eliud Kipchoge finished in 2.03 hours. What was his average speed? π 42.2 −1 π£= = = 20.8 km hr π‘ 2.03 Marathon Runners are FAST Instantaneous vs Average Eliud Kipchoge average speed was worked out to be 20.8 km hr −1 . Does this mean that his speed was 20.8 km hr −1 at every instant of the race? Instantaneous vs Average It should be noticed that the average value (over a period of time) is very different to the instantaneous value (at one particular time). Instantaneous vs Average Instantaneous vs Average Instantaneous vs Average Racing against Usain… In 2012, Usain Bolt’s Gold Medal 100 metere dash took just 9.63 seconds. In 1896, the gold medalist finished in 12.00 seconds. Making the assumption that they are traveling at a constant velocity (they aren’t really), how far behind Usain would the 1896 medalist be? Racing against Usain… In 2012, Usain Bolt’s Gold Medal 100 metre dash took just 9.63 seconds. In 1896, the gold medalist finished in 12.00 seconds. Making the assumption that they are traveling at a constant velocity (they aren’t really), how far behind Usain would the 1896 medalist be? Method 1: 9.63 100 − 100 = ππ. ππ π¦ 12 Method 2: 100 = 8.3 m s−1 12 8.3 m s −1 9.63 s = 80.25 m 100 − 80.25 = ππ. ππ π¦ Plot this problem on a D vs T graph Displacement (m) 120 100 80 60 40 20 1 2 3 4 5 6 7 8 Time (s) 9 10 11 12 Plot this problem on a D vs T graph Displacement (m) 120 100 80.25 m 80 60 40 20 1 2 3 4 5 6 7 8 Time (s) 9 10 11 12 Racing against Usain… Plot this problem on a D vs T graph Let’s take a look at the D vs T graph again If we were not presented with the values in a problem, how could we use the graph to determine the average velocities of both runners? Plot this problem on a D vs T graph Let’s take a look at the D vs T graph again If we were not presented with the values in a problem, how could we use the graph to determine the average velocities of both runners? The gradient of a displacement-time graph is the velocity. Is there anything useful represented by the area underneath the D v T graph? Plot this problem on a D vs T graph Let’s take a look at the D vs T graph again If we were not presented with the values in a problem, how could we use the graph to determine the average velocities of both runners? The gradient of a displacement-time graph is the velocity. Is there anything useful represented by the area underneath the D v T graph? NO! Plot this problem on a D vs T graph Is there anything useful represented by the area underneath the D v T graph? NO! IB SL Exam Nov 2017 Constant Positive Velocity Velocity (m s-1) Displacement (m) Changing position at a constant rate forward Time (s) Time (s) Constant Positive Velocity Velocity (m s-1) Displacement (m) Changing position at a constant rate forward Time (s) Time (s) Constant Negative Velocity Velocity (m s-1) Displacement (m) Changing position at a constant rate backward Time (s) Time (s) Constant Negative Velocity Velocity (m s-1) Displacement (m) Changing position at a constant rate backward Time (s) Time (s) Plotting Displacement vs Time Displacement (m) Runner A Runner B Runner C Which runner was moving the fastest? Time (s) Plotting Displacement vs Time Displacement (m) Runner A Runner B Runner C Steeper Slope Which runner was moving the fastest? Time (s) Constant Velocity Displacement/Distance-Time graph • Objects moving with constant velocity produce a linear graph. • The gradient of the graph is the velocity Velocity-Time graph • An object moving with constant velocity produces a horizontal linear graph with slope zero. IB Practice Question IB Practice Question Do you know which car is the fastest in the world? Do you know which car is the fastest in the world? Koenigsegg Agera Dodge Challenger SRT Demon Do you know which car is the fastest in the world? Koenigsegg Agera Top speed: 439 km/h Dodge Challenger SRT Demon Top speed: 326.70 km/h Do you know which car is the fastest in the world? Koenigsegg Agera Top speed: 439 km/h 0-100km/h in 2.8 seconds Dodge Challenger SRT Demon Top speed: 326.70 km/h 0-100 km/h in 2.1 seconds What is… Velocity Acceleration What is… Velocity the rate of change of displacement with respect to time Acceleration the rate of change of velocity (NOT JUST SPEED) with respect to time Types of Acceleration Types of Acceleration Speeding Up Slowing Down Changing Direction Average Acceleration a = βv / βt a = (v – u) / t acceleration where v is the final velocity and u is the initial velocity FYI ο·Many textbooks use βv = vf - vi for change in velocity, vf for final velocity and vi initial velocity. IB gets away from the subscripting mess by choosing v for final velocity and u for initial velocity. a = βv / βt a = (v – u) / t π= acceleration where v is the final velocity and u is the initial velocity π£−π’ π‘ π= 400 − 0 0.001 π = 400000 m/s2 Calculate the acceleration of a bullet that changes speed from 0 to 400 m/s in 0.001 s. a = βv / βt a = (v – u) / t acceleration where v is the final velocity and u is the initial velocity π£ = π’ + ππ‘ π£ = 0 + (7 x 4) π£ = 28 m/s Calculate the final speed of a cheetah that accelerates from rest at 7 m/s2 for 4 s. a = βv / βt a = (v – u) / t π= π= acceleration where v is the final velocity and u is the initial velocity π£−π’ π‘ −0.6 − (1.0) 0.01 2 , right of2 screen π = 160 m/s π= −160 m/s Calculate the acceleration of a billiard ball that changes velocity from 1.0 m/s, left to 0.6 m/s, right in 0.01 s. IB Practice Question IB Practice Question Acceleration Velocity (m s-1) 30 25 0-30 m s-1 in 10 seconds 20 15 10 5 0-30 m s-1 in 2.5 seconds 1 2 3 4 5 6 7 8 Time (s) 9 10 11 12 Acceleration Velocity (m s-1) 30 25 0-30 m s-1 in 10 seconds 20 15 m s −1 π ππππ = = π¦ π¬ −π s 10 5 1 2 3 4 5 6 7 8 Time (s) 9 10 11 12 0-30 m s-1 in 2.5 seconds Acceleration Velocity-time graph • The gradient of a velocity-time graph is the acceleration. • A constantly (uniformly) accelerating object produces a linear graph Acceleration What about displacement? Can we find this out from the graph? Acceleration Velocity-time graph • The area underneath the graph is the displacement Area = 0.5 × 10 × 30 = 150 m Area = 0.5 × 2.5 × 30 = 37.5 m 6 B 5 C Average acceleration between A and B 4 3 Gradient = βπ¦ βπ₯ Gradient = rise run Gradient = βπ£ βπ‘ Gradient = π¦2 − π¦1 π₯2 − π₯1 Gradient = 5−0 10 − 5 Gradient = 1 m/s2 Velocity (m/s) 2 1 A D 0 -1 -2 -3 -4 E -5 F -6 0 10 20 30 Time (s) 40 50 60 6 B 5 C Distance travelled between A and F 4 πβ 5x5 π AB =Average = 2 speed = 12.5 m 2 between A and F 3 Velocity (m/s) 2 1 A π BC = π€π = 5 x 30 = 150 m π π£ = πβ 5x5 π = = π‘ = 12.5 m D 0 CD -1 π DE = -2 2 2 237.5 12.5 m πβπ£ =5 x 5 = 2 55 = 2 π£ = 4.32 m/s π EF = π€π = 5 x 10 = 50 m -3 -4 E -5 F -6 0 10 20 30 Time (s) 40 50 60 π = 12.5 + 150 + 12.5 +12.5 + 50 = 237.5 m 6 B 5 C Displacement between A and F 4 3 π AB = Velocity (m/s) 2 π BC 1 A D 0 π CD 5x5 2 2 = 2 = 12.5 m Average velocity between A and F = π€π = 5 x 30 = 150 m π πβ π£ 5=x 5 π‘ = 12.5 m = = -1 π DE = -2 πβ 2 πβ 2 112.5 5 x −5 =π£ =2 55 = −12.5 m = 2.04 π EF = π€π =π£ −5 x 10 m/s = −50 m -3 -4 E -5 F -6 0 10 20 30 Time (s) 40 50 60 π = 12.5 + 150 + 12.5 −12.5 − 50 = 112.5 m IB Practice Question IB Practice Question Constant Positive Acceleration Velocity (m s-1) Displacement (m) Changing velocity by speeding up at a constant rate Time (s) Time (s) Constant Negative Acceleration Velocity (m s-1) Displacement (m) Changing velocity by slowing down at a constant rate Time (s) Time (s) Acceleration Displacement/Distance-Time graph • An object moving with constant (uniform) acceleration produces a parabolic graph with an increasing slope Velocity-Time graph • A constantly (uniformly accelerating) object produces a linear graph • The gradient of a velocity-time graph is the acceleration. IB Practice Question IB Practice Question Acceleration-Time Graphs • A graph of acceleration (y-axis) against time (x-axis). • Used to calculate the change in velocity and instantaneous acceleration of an object. B 14 12 10 8 Acceleration (m/s2) 6 Change in velocity A and B between C D 4 C D πβ Area Area== π€π 2 Area = rise x run run x rise Area = Area = π x π‘ 2 2 0 A -2 14 Area Area== 25xx10 2 Area = 20 m/s Area = 35 m/s -4 -6 -8 -10 -12 0 5 10 15 20 25 Time (s) 30 35 40 4 5 IB Practice Question IB Practice Question IB Practice Question IB Practice Question Recap Definitions Displacement Velocity Speed Acceleration Symbol Definition SI Unit Vector or Scalar π change in position m Vector π£ or π’ rate of change of displacement π π£= π‘ m.s-1 Vector π£ or π’ rate of change of distance π π£= π‘ π rate of change of velocity π£−π’ π= π‘ m.s-1 m.s-2 Scalar Vector Recap Motion Graphs Displacement-Time Graphs • The gradient of a displacement-time graph is the velocity • The area underneath a displacement-time graph does not represent anything useful Velocity-Time Graphs • The gradient of a velocity-time graph is the acceleration • The area under a velocity-time graph is the displacement Acceleration Time Graphs • The gradient of an acceleration time graph is not often useful (it is the rate of change of the acceleration) • The area under an acceleration time graph is the change in velocity. * Remember to always look at the axes of the graph carefully in order to avoid mistakes!
