Question

Question 1 This question is worth 20 marks and is designed to test your understanding of motion in one dimension (Unit 1). A train makes a journey from Oxford to Didcot along a completely straight track. It leaves Oxford at time t = 0. Table 1 below shows the velocity Ur of the train at various times t for the whole journey. Table 1 For use with Question 1. t/s U/ms- 40 480 520 560 600 (a) (i) Plot a graph of vx against t (use graph paper if you produce the plot by hand). (8 marks) (ii) Using your graph, estimate the distance between Oxford and Didcot. (4 marks) (b) Using your graph of vx against t to help you, sketch (not on graph paper) a graph of the distance travelled by the train against time for the whole journey. You do not need to calculate any actual distances for this sketch but you should concentrate on getting the general shape correct and each axis should have an indication of the scale. (8 marks)

Answer 1

i.  

Velocity-time graph Velocity (m/s) 1 2 3 4 5 6 7 10 11 12 13 8 9 Time (s) 14 15 16 do Go to Settings to actis

ii.
Distance between Oxford and Didcot is the area under the velocity-time graph. Using excel, area of the graph can be found by adding the areas of rectangles and trapeziums. Other way is to find distance for each time and sum all for all the time points. s = (v2 =) (t2-t) where s is the distance travelled between (t, - t).

Time (s) Velocity (m/s) Distance travelled (m) Distance (m) 120 0 360 40 80 120 160 20 28 200 240 40 40 40 640 960 1280 1520 1600 1600 1600 1560 1360 1000 600 280 80 280 320 360 400 440 480 520 480 1120 2080 3360 4880 6480 8080 9680 11240 12600 13600 14200 14480 14560 14560 40 38 30 20 10 560 600 0 Total distance = 14560

iii.

Distance-time graph 16000 14000 12000 10000 Distance (m) 8000 6000 4000 2000 1 2 3 4 5 6 7 8 9 Time (s) 10 11 12 13 14 15 16