Motion in a straight line

The equations governing the motion of a body in a straight line are best derived by calculus. If any of the three relations distance-time, velocity-time and acceleration-time are known in mathematical form, the others may be obtained by differentiation or integration as appropriate, since <math display='block'> <mrow> <mfrac> <mi>d</mi> <mrow> <mi>d</mi><mi>t</mi></mrow> </mfrac> <mo stretchy='false'>(</mo><mi>d</mi><mi>i</mi><mi>s</mi><mi>tan</mi><mi>c</mi><mi>e</mi><mo stretchy='false'>)</mo><mo>=</mo><mi>v</mi><mi>e</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>t</mi><mi>y</mi></mrow> </math>]]</EquationSource><EquationSource Format="TEX"> <![CDATA[\frac{d}{{dt}}(dis\tan ce) = velocity and <math display='block'> <mrow> <mfrac> <mi>d</mi> <mrow> <mi>d</mi><mi>t</mi></mrow> </mfrac> <mo stretchy='false'>(</mo><mi>v</mi><mi>e</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy='false'>)</mo><mo>=</mo><mi>a</mi><mi>c</mi><mi>c</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>.</mo></mrow> </math>]]</EquationSource><EquationSource Format="TEX"> <![CDATA[\frac{d}{{dt}}(velocity) = acceleration. Alternatively, graphical methods may be used, especially if a precise mathematical relation cannot be found. The set of graphs shown in Fig. 52 refer to the motion of a horse during a race, and it may be seen how the significant features of each graph relate to the others.