A cyclist : starts from rest and travels with constant acceleration for 1 second to reach a velocity of 2m/s They travel at this velocity for 3 seconds , before accelerating ; at a constant rate to 13m/s over 11 seconds. Which of the lines A-F complete the velocity-time graph of the cyclist's journey?

## Step 1: The graph is in two dimensions with velocity (v) on the y - axis and time (t) in seconds(s) on the x - axis. The cyclist starts from rest. This points us to the fact that he starts from ## Step 2: He travels with constant acceleration for 1 second to reach a velocity of .which means that after this 1 second he would have covered 2 control units measured on the y-axis and 1 control+b19 unit on the x axis. This linear movement can be denoted by a line creating angle less than 90 degrees with time which is our x – axis and with start at 0 second and y-axis. ## Step 3: He travels at this velocity for 3 seconds , this will be represented by a line parallel to time axis , as the velocity has not changed for that interval of time (1s to 4s).## Step 4: The cyclist then accelerates at a constant rate to over 11 seconds. This starts from where previous stage finished (at 4,2) We are provided with the end velocity and the time it took to reach there, this gives us the slope of the line to the known to the point on same y – axis higher points on it, this slope inspiration completes line from again points o time axis to join a y – axis except to the previous portion and the time line irrespective to from where last finished is from 4s to 15s . The velocity increased as he started to accelerate so this should indicate a farther rise in measured height of line given with respect to y – axis.