Assume an object is moving along a straight line with the velocity {{MATH_26}}, for {{MATH_27}}, where {{MATH_28}} is measured in seconds, and {{MATH_29}} in {{MATH_30}}. Find the displacement of the object over the time interval {{MATH_31}}. {{CMD_32}} Since we know how to compute the displacement when the velocity is constant, we will start by asuming that the velocity is constant and equal to {{MATH_33}}, the initial velocity, for the entire four-second time interval, {{MATH_34}}. This scenario will give us a very rough approximation of the displacement, but it is a good starting point. {{MATH_35}} This scenario is illustrated in the figure below. {{CMD_36}} {{ENV_37}} {{CMD_38}} {{COMMENT_39}} {{COMMENT_40}} {{COMMENT_41}} {{COMMENT_42}} {{COMMENT_43}} {{COMMENT_44}} {{COMMENT_45}} {{COMMENT_46}} {{COMMENT_47}} {{COMMENT_48}} {{COMMENT_49}} {{COMMENT_50}} {{COMMENT_51}} {{COMMENT_52}} {{COMMENT_53}} {{COMMENT_54}} {{COMMENT_55}} {{COMMENT_56}} {{COMMENT_57}} {{COMMENT_58}} {{COMMENT_59}} {{COMMENT_60}} {{COMMENT_61}} {{COMMENT_62}} {{COMMENT_63}} {{COMMENT_64}} {{COMMENT_65}} {{COMMENT_66}} {{COMMENT_67}} {{COMMENT_68}} {{COMMENT_69}} {{COMMENT_70}} {{COMMENT_71}} {{COMMENT_72}} {{COMMENT_73}} {{COMMENT_74}} {{COMMENT_75}} {{COMMENT_76}} {{COMMENT_77}} {{COMMENT_78}} {{COMMENT_79}} {{COMMENT_80}} {{COMMENT_81}} {{COMMENT_82}} {{COMMENT_83}} {{COMMENT_84}} {{COMMENT_85}} {{COMMENT_86}} {{COMMENT_87}} {{COMMENT_88}} {{COMMENT_89}} {{COMMENT_90}} {{COMMENT_91}} {{COMMENT_92}} {{COMMENT_93}} {{COMMENT_94}} {{COMMENT_95}} {{COMMENT_96}} {{COMMENT_97}} {{COMMENT_98}} {{COMMENT_99}} {{COMMENT_100}} {{COMMENT_101}} {{COMMENT_102}} {{COMMENT_103}} {{COMMENT_104}} {{COMMENT_105}} {{COMMENT_106}} {{COMMENT_107}} {{COMMENT_108}} {{COMMENT_109}} {{COMMENT_110}} {{COMMENT_111}} {{COMMENT_112}} {{COMMENT_113}} {{COMMENT_114}} {{COMMENT_115}} {{COMMENT_116}} {{COMMENT_117}} {{COMMENT_118}} {{COMMENT_119}} {{COMMENT_120}} {{COMMENT_121}} {{COMMENT_122}} {{COMMENT_123}} {{COMMENT_124}} {{COMMENT_125}} {{COMMENT_126}} {{COMMENT_127}} {{COMMENT_128}} {{COMMENT_129}} {{COMMENT_130}} {{COMMENT_131}} {{COMMENT_132}} {{COMMENT_133}} {{COMMENT_134}} {{COMMENT_135}} {{COMMENT_136}} {{COMMENT_137}} {{COMMENT_138}} {{COMMENT_139}} {{COMMENT_140}} {{COMMENT_141}} {{COMMENT_142}} {{COMMENT_143}} {{COMMENT_144}} {{COMMENT_145}} {{COMMENT_146}} {{COMMENT_147}} {{COMMENT_148}} {{COMMENT_149}} {{COMMENT_150}} {{COMMENT_151}} {{COMMENT_152}} {{COMMENT_153}} {{COMMENT_154}} {{COMMENT_155}} {{COMMENT_156}} {{COMMENT_157}} {{COMMENT_158}} {{COMMENT_159}} {{COMMENT_160}} {{COMMENT_161}} {{COMMENT_162}} {{COMMENT_163}} From the graph above, we see that the assumption of constant velocity is not quite accurate. The velocity is changing, so we should allow our velocity to change as well. Instead of assuming the velocity is constant over the entire four-second interval, we will keep approximating the velocity with a constant over smaller and smaller intervals of time.