A car is initially stationary. At time to it starts to move at speed v for a time At. Immediately after this it moves at speed u > for a time At < At. After this time it is stationary again. (a) Using this information sketch a graph of speed u versus time t. Label all axes sufficiently so that the graph is quantitatively accurate. (b) From your graph determine the average speed (v), of the car while it is moving. Express (v), as a formula using the symbols v, At1, U2, At. (u), is known as the time weighted average. Compute a numerical value for (v)t given the following: U = 1ms , At = 2s, = 2 ms, At = 18, to = 0 s v (c) Now draw a graph of speed u versus distance s using the numerical values for speeds and times given in section (b) and label the axes as before. (d) From the second graph find the average speed (v), known as the distance weighted average. Again express (v), as a formula using the symbols v, AS1, 02, AS2, where Asi and Asi are the distances that the car travels at and 2. Also provide a numerical value for (v), using the values given in section (b) (e) Which of the two averages (v), or (u), is equivalent to the conventional definition of average speed which we assume to be (v)e = total distance travelled? (f) State the mathematical operation that should be applied to the curve of v(t) to compute (v)e if we assume v to be any function of time or distance. [1] [2] [1] [2] [1] [1]