A test car travels in a straight line along the x- axis. The graph in ?Fig. E2.11 shows the car’s position x as a function of time. Find its instantaneous velocity at points A through G.
Answer: Step 1: We can calculate the instantaneous velocity at any point is the slope of the tangent line to the graph at that point. For the Fig. E2.11 Step2 : Portion of the curve on which A and B lies appears to be approximately a line segment. So, we can find the slope of line. Which give the instantaneous velocity at the point Step 3: Calculating the instantaneous velocity of point “A” and “B” From the graph ; Slope of the graph = rise /run = 15/ 2.1= 7.1 m/s ( instantaneous velocity) Step 4: At C the instantaneous velocity there to be 0. As there is no slope at point C. From the graph : Slope of the graph = rise /run = -40/1 = -40 m/s Step 6: calculating the slope at point G , where G is having a curve i.e function , so we can draw a tangent at point G at whatever the slope of that line we can say that will be the slope of that point G Now if we draw a tangent at point G it will be parallel to the timeline. It shows that it's parallel to line C Therefore it doesn't have any slope i.e slope = 0