Distance-­‐Time and Speed-­‐Time Graphs O-­‐Level E. Math Reference Notes Distance-­‐Speed-­‐Time Graph Distance The distance of the object from a reference point at any point in time is read from the axes Speed The gradient of the distance-­‐time graph represents the speed of the of the object Larger gradient à Greater speed Smaller gradient à Slower speed Zero gradient à Zero speed Negative gradient à Object is moving in opposite direction from its initial fdsafdsafdasfdasfdafdsafdsadirection of travel Object not moving; Distance from O Zero gradient à zero speed Object is moving away from O; Constant gradient à Constant speed Object is moving back towards O; Constant gradient à Constant speed Time Speed-­‐Time Graph Speed The speed of the object at any point in time is read from the axes Acceleration The gradient of the distance-­‐time graph represents the speed of the of the object Larger gradient à Greater acceleration Lower gradient à Slower acceleration Zero gradient à Positive gradient à Negative gradient à 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
Constant speed Object is accelerating (Speed is increasing) Object is decelerating (Speed is decreasing) 𝐹𝑖𝑛𝑎𝑙 𝑠𝑝𝑒𝑒𝑑 − 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑠𝑝𝑒𝑒𝑑
𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
Distance The area under the graph represents the distance travelled by the object. Speed Increasing speed Constant gradient à Constant acceleration Constant speed Area under the graph = Distance travelled Decreasing speed Constant gradient à Constant deceleration Time KiX Education Singapore www.kix.sg Distance-­‐Time and Speed-­‐Time Graphs O-­‐Level E. Math Reference Notes Comparison of distance-­‐time graph and speed-­‐time graph Distance from O Distance-­‐Time Graph Corresponding Speed-­‐Time Graph Speed Time First part: Constant gradient Second part: Zero gradient Third part: Constant gradient Distance from O Increasing gradient Distance from O Decreasing gradient KiX Education Singapore Time First part: Constant speed Second part: Zero speed Third part: Constant speed Speed Time Increasing speed Speed Time Decreasing speed Time Time www.kix.sg