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Distance Time Velocity Gizmo Handout-2

Interactive exploration comparing distance-time and velocity-time graphs. Students analyze motion, displacement, and speed using visual data to understand differences between distance traveled and change in position.

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    |||| Gizmos Marne: Cate: Stu de nt ExpIoration: Di sta nce-Time a n d Velocity-Time Graph s Directions: Follow the instructions to go through the srnuiation. Respond to the questions and prompts in the orange bortes. /NOTE TO TEACHERS 4AC STUDENTS: This fesson was designed es a foAtw-up fo the Distance-Time Graces Gcmc. Wfereowrvnsidyxj ro.Tp'ere that aciiwSybefore this oneJ Vocabulary: displacement, distance traveed, slope, speed, velocity Prior Knowledge Questions (Do these BEFO?E using the Gzmo.} Dora runs one lap around tie track, finishing wnere she started. Clark runs a 1ZOmeler dash along the straignt side of die track. ZJarz iza an attire Zap armxd the track rS'jItiES IE ter nr-nni-qn a CiitmiCE of +jta compered to Clara's ICOm dittzcce. As Dora traveled a sreater distzrce than Clark AJi-nouzn Ewa ran a further distance she arrived ar the same position sbe started makzis her Lave a displacement of Cm On ths other hand Clark moved UXtna from his start fire makinghum hate a displacement of + - lC£m and thru Levins a greater change in positon. 1. Which runner traveled a greater distance? 2. 'Mikih runner ha: a greater change in position, start to finish? Gizmo Warm-up The Distance-Tme Graphs Gizmo shows a dynamic graph of the position of a runner over time. Tne Defence-Tine and Vebcily- Time Graphs Gizmo ndudes tnat same graph and adds two new ones: a velocity vs. time graph ard a distance traveled vs. time graph. The graph snown below (and in the Gizmo) shows a runner's position {ord stance from the starting lire) over time. This is most commonly called a posrtian-fvne graph. I I 1" i 4 ii Check that tne Number of Points is 2. Turn an Show graph ard Show animation for both Runner 1 ard Runner 2. 1. Drag the points tn create the yaph shown to the right. • Runner Ts ne i'the r ed one) should have endpoints at t'O, O'i and (4. 40). ■ Runner 2's ne (the blue one) should have endpo nts at {0, 40} and (4. 20}. RBVnd.d3Dfi Far K-ciic-oJ jia o N y Pubic i h a m g sr poitrt-- jrcNso-:. -Z ZC3U

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    2. Click the : reen Start button on the stopwatch. Watch toe two rLnners carefiity. I r what Mo ways are the nunne r s' motions a fferent? R j n n e r l initiates a u n i f o r m m o t i o n with a constant velocity of +1 Dm/s.. as evidenced by the grep n depicting a consistent increase in the distance between the runner and the start line o v e r t i m e . Conversely, Runner 2 is moving tows rds the start line at a slower pace 'with a u n i f o r m motion o f - 5 m / s . The graph illustrates a Diminishing d i s t a n c e between Runner 2 and toe start line as time progresses, c o n f i r m i n g the slower pace. By calculating toe slopes for both runners and observing their constancy, it became evident that both were maintaining a u n i f o r m m o t i o n . Activity A: Velocity-time graphs Get toe Giznc reacy: ■ Click the red Reset button on toe stopwatch. - Change the Number of Points 1o 5. ■ Turn off Show graph ard Show animation for Runner 2. H -23 — Speed is a measure of how fast an object moves, regard ess of direction. Speed can rever be negative. Velocity describes both speed and direction, ard can be positive or negative. 1. In toe Gizmo, make a position-time graph far Ru nner 1 with toe follow ng features: • Tnere is at least one major change in speed. - Tnere is at least one major change in direction . Cfck the green Start button and watch toe runrer Tin. Adjust your graph if needed to tree: the requ ’ements. Hand draw in tois space or dick here to select EDIT to use the drawing tool. Sketch your graph to the right. 2. VWiere was the runner each second? Sased on your graph, fill in all except die final column in the table below. {Leave the velocity cdLmn dank for now.) Label any numbers with units. Time P o s i t i o n at end of time interval (m) Distance moved this time interval |m) To the left or right? Velocity this time interval (mJs) 0 - 1 sec 4Dm E m Right tSCm's 1 - 2 sec 3Dm ’Cm Left -1Dmfe 2 - 3 sec 2Dm "Cm Left -1Drn |, s 3 - 4 sec 3Dm 10m Right t l & n ' s uctDH ci •c-cw'jc-rn u » orty. P-.b-fc afrin-a or faaatng prahtHM. — 2272 EapcraUavnrnj " Al r iti rra~. K

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    3. To calculate the velocity for each tme nterval, first calcu ate the speed of the turner in tnat interval (speed = distance + time). If the direction is left to right, velocity is positive. If the direction is r g h t l o left, velocity is reg alive. Fill in the velocity column of the tab e above. Use units (rrVs). Wren this runner is running to the left (negative velocity), what dies his position-time g r aph look like? As the ninner mores to the left, tne graph descends towards the x-axis. indicating a decrease in d stance from the starting line. Notably, when heading towards the start line, the s lope of the graph b e c o m e s negative, in c o n t r a s t to the positive slope when m o v i n g away from the start line. This negative slope aligns with the negative velocity, signifying m o v e m e n t to tne left Tne observation that speed, represented by the slope, corresponds to tne velocity, which e n c o m p a s s e s bctn speed and direction, further emphasizes the l o g i c a l consistency of the negative slope 'when the runner is headed towards tne start line. 4. Slope is the steepness Of a grach. To fird the slope of a line, divide the charge in y-vai ue (rise) by the change inx-value (rim). Likevebcty, slope can be positive, zero, or negative. Fill in the s ope of each segment of your posilior-t me graph, along with tne runner's velocity during each time interva . in the taele beew. Time i nterval Slope Velocity (mi's) 0 sec - T sec +30 +30ms 1 sec - 7 sec -10 -10m's 2 sec - 3 sac -10 -10m's 3 sec - 4 sac +10 +10m's 5. Exam ne your velodtes and the position-time grajdn you made. Hovj is the slope of a positon-time grach related to the velocity of tne runner? Slope can give us the numeral value for velocity as shown above and 1he slope teing positive or negat ve tells us if the velocry is positive or negative.

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