Graphs of Motion Investigation Aim To investigate the relationships between displacement, velocity, acceleration and time for CONSTANT VELOCITY and ACCELERATED motion. Task 1. By making use of data logging equipment, produce graphs of displacement vs time, velocity vs time acceleration vs time for motion at CONSTANT VELOCITY and constant ACCELERATION. Describe the relationship observed in each graph in words. Calculate values for displacement, velocity and acceleration using data from graphs.

Graph Skills y The gradient (slope) of a straight line graph is constant and can be found by taking the coordinates between any two points. The gradient of a curve changes continually. At any point the gradient is found by taking the gradient of a tangent to the curve at that point. y x y2 - y1 x2 - x1 Grad = = y2 2 (x2;y2) y y1 x 1(x1,y1) x x1 x2 y x y2 - y1 x2 - x1 2 (x2;y2) Gradat x = = y 1(x1,y1) x x

Constant Velocity Example Assume you walked for 5s covering 1meter every second. Time (S): 0| 1 | 2 | 3 | 4 | 5 | X (m): 0| 1 | 2 | 3 | 4 | 5 | time (s) Displacement (m) Average Velocity (m/s) Instantaneous Velocity (m/s) Acceleration (m/s2) 1 2 3 4 5

Displacement vs. time - 5 4 3 2 1 s (m) I I I I I t (s) 0 1 2 3 4 5

Displacement vs. time S (m) t (s) 5 5 The displacement time graph for constant velocity motion is a ………….line. (Positive or Negative slope) Now calculate the GRADIENT of this graph. GRADIENT = m = /\y/ /\x = …/… = … m/s = ........................! Gradient of displacement vs time graph equals the ………………. of the motion.

Velocity vs. time 2 1 v (m/s) I I I I I t (s) 0 1 2 3 4 5

Graphs of Motion Investigation Aim To investigate the relationships between displacement, velocity, acceleration and time for CONSTANT VELOCITY and ACCELERATED motion. Task 1. By making use of data logging equipment, produce graphs of displacement vs time, velocity vs time acceleration vs time for motion at CONSTANT VELOCITY and constant ACCELERATION. 2. To describe the relationship observed in each graph in words.

Graph Skills y y x y2 - y1 x2 - x1 The ……..…… (……..) of a straight line graph is …………. and can be found using the coordinates between any two points. The gradient of a curve ………………………. continually. At any point the gradient is found by taking the gradient of a ……………….. to the curve at that point. Grad = = y2 2 (x2;y2) y y1 x 1(x1,y1) x x1 x2 y x y2 - y1 x2 - x1 2 (x2;y2) Gradat x = = y 1(x1,y1) x x

Velocity vs. time Area = l x b = 1x5 = 5 (m.s-1 )(s) = m Area = 5m

Velocity vs. time m = /\y/ /\x = …/… = … m/s2 AREA = ………………………….. 1 v (m/s) t (s) 5 Now calculate the GRADIENT and AREA of this graph. m = /\y/ /\x = …/… = … m/s2 Gradient = …………………….. AREA = L x b = …. x …. = ….. m (…..)X…. AREA = …………………………..

DISPLACEMENT - TIME Graph SKETCH GRAPHS - Constant Velocity 1 2 ... . . . . . . . . . . . . . . . . . . . . . . . . . .. . .... S1 S2 Displacement increases by same amount in equal time intervals. time/(s) 0 1 2 3 4 5 6 7 8 9 10 DISPLACEMENT - TIME Graph VELOCITY - TIME Graph s/(m) 2. v/(m/s) . 1. 2. GRADIENT = ……….. . s2 . AREA = ………….. 1. s1 t1 t2 t/(s) t/(s) The ……………… between any two points on the VELOCITY - TIME graph equals the objects displacement between the two points. The ……………………of the DISPLACEMENT vs TIME graph equals the velocity of the object. (at any point)

Constant Acceleration Assume you started from rest but traveled further every second. Time (S): 0| 1 | 2 | 3 | 4 | 5 | S (m): 0| 0.5| 1.5 | 2.5 | 3.5 | 4.5 | t(s) X (m) Vav Vi a 1 0.5 2 3 4.5 4 8 5 12.5 Calculate aV -Average velocity Instantaneous velocity Acceleration

Constant Acceleration

SKETCH GRAPHS - Constant ACCELERATION 1 2 .... . . . . . . . . . . S1 S2 time/(s) 0 1 2 3 4 5 6 7 8 9 10 Displacement increases by (uniformly ) increasing amounts in equal time intervals. ACCELERATION - TIME DISPLACEMENT - TIME VELOCITY - TIME v (m/s) a (m/s2) s2 s/(m) GRAD = … GRAD = …. s1 t1 t t/(s) t2 t/(s) t/(s) The gradient of the displacement vs time graph (tangent - at any point) gives the ……………..of the object at that point. The gradient of the velocity vs time graph (at any point) gives the ……………….of the object.

SKETCH GRAPHS - Constant ACCELERATION 1 2 -- - - - - - - - - --> Displacement increases by (uniformly ) increasing amounts in equal time intervals. DISPLACEMENT - TIME VELOCITY - TIME ACCELERATION - TIME s/(m) v (m/s) 2. a (m/s2) 2. 1. 2. 1/2bxh AREA = … AREA = …(av) l x h 1. s s2 1. s1 l x h t2 t2 t1 t2 t/(s) t1 t/(s) t1 t/(s) The AREA of the acceleration vs time graph (between any 2 points) gives the …………… ……………… of the object between the two points. The AREA under the VELOCITY vs time graph (between any 2 points) gives the ………………… of the object between the points.

SKETCH GRAPHS - Summary 1 2 -- - - - - - - - - --> DISPLACEMENT - TIME VELOCITY - TIME ACCELERATION - TIME v (m/s) a (m/s2) 2. s/(m) 1. 2. 1. t1 t2 t/(s) t1 t/(s) t2 t/(s) Gradient of the displacement vs time graph gives the …………….. AREA under the VELOCITY vs time graph gives the ……………………. …………….. of the acceleration vs time graph gives the average velocity. ……………… of the velocity vs time graph gives the acceleration of the object.

Graphs of Motion A - acceleration (+) B - constant velocity (+) C - deceleration (+) D - stationary E - reverse acceleration (-) F - reverse constant v (-) G - reverse deceleration (-) ... . . . . . . . s . . . . . . . . t . . . . . . . ... v . t . . . . . .. a . . . . . . . . . t ... . . . . . . .

SKETCH GRAPHS - Displacement vs Time ........................................ . . . . . . . . Constant Velocity Constant Acceleration s/(m) s/(m) t/(s) t/(s) ……………………………… ………………….displacement per second - ……………… increases.. . . . . . .... ............................ Stationery Object Deceleration. Object moves backwards. s (m) s (m) s (m) t/(s) t/(s) t/(s) …………………………….. displacement ………………. - slowing down. Displacement is being…………………(…….. …………………………………….). ………………….. ……………………

SKETCH GRAPHS - Velocity vs Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v/(m) v/(m) t/(s) t/(s) . . . . . . .. . . . . . . . .. . . Constant deceleration. v (m) v (m) v (m) t/(s) t/(s) t/(s) Object ………………. ………………………. v = 0 …………………………

SKETCH GRAPHS - Task Draw sketch graphs of displacement vs time, velocity vs time and acceleration vs time for a car that starts off from rest, accelerates uniformly for 5s, attains a speed of 30m/s which it maintains for 10s. The car then slows down for 15s at which point it comes to a halt. Indicate as much detail on the graphs as possible. s/(m) a/(m/s2) v/(m/s) t/(s) t/(s) t/(s)

SKETCH GRAPHS - Example Tut on Graphs & equations 8 | 0 10 20 30 40 12

Graphs of two motions. The graph shows the speeds of two cars A & B as a function of time. What is the difference in the distances traveled by A & B after 20 s? (7) After how many seconds will A & B have traveled the same distance? (6) Calculate the acceleration of A. (4) v A 6 5 B 10 15 20 t (s)

Graphs of Vertical Motion An object is thrown vertically up and returns to the thrower’s hand. 10 20 30 -10 -20 -30 V (m/s) -10 -20 -30 30 20 10 X a V t t t