 Physics Help Forum Why total time taken s₁/v₁ + s₂/v₂ + s₃/v₃ in average speed?
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 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum Jul 18th 2018, 09:03 AM #1 Junior Member   Join Date: Jul 2018 Posts: 22 Why total time taken s₁/v₁ + s₂/v₂ + s₃/v₃ in average speed? As we know the Average speed = Total distance / Total time but why in the case below Distance traveled = s₁ + s₂ + s₃ and total time taken = s₁/v₁ + s₂/v₂ + s₃/v₃ How is it possible? Could you explain please? so, altogether Vav = s₁ + s₂ + s₃ / ( s₁/v₁ + s₂/v₂ + s₃/v₃)   Jul 18th 2018, 09:58 AM #2 Senior Member   Join Date: Oct 2017 Location: Glasgow Posts: 426 speed = distance / time Therefore, time = distance/speed Let's assign some symbols to these quantities... time = t speed = v (from 'velocity') distance = s (don't ask... people just like using s for distance. it crops up a lot in maths too for path lengths and things like that) The equation above described in symbols is: $\displaystyle t = \frac{s}{v}$ Let's use the numbers 1, 2 and 3 to designate the three parts of a journey. These are called "indices". Time for first part of journey: $\displaystyle t_1 = \frac{s_1}{v_1}$ Time for second part of journey: $\displaystyle t_2 = \frac{s_2}{v_2}$ Time for third part of journey: $\displaystyle t_3 = \frac{s_3}{v_3}$ Total time for journey: $\displaystyle t_{total} = t_1 + t_2 + t_3$ Substitute for individual times, we get: $\displaystyle t_{total} = \frac{s_1}{v_1} + \frac{s_2}{v_2} + \frac{s_3}{v_3}$ The total distance is: $\displaystyle s_{total} = s_1 + s_2 + s_3$ Therefore, the average speed is: $\displaystyle \bar{v} = \frac{s_{total}}{t_{total}} = \frac{s_1 + s_2 + s_3}{\frac{s_1}{v_1} + \frac{s_2}{v_2} + \frac{s_3}{v_3}}$ Indranil likes this.  Tags average, s₁ or v₁, s₂ or v₂, s₃ or v₃, s₁ or v₁, s₂ or v₂, speed, time, total Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post hexrei General Physics 2 Oct 1st 2016 08:58 AM Punch Kinematics and Dynamics 13 Mar 20th 2010 07:28 AM alessandro Theoretical Physics 1 Feb 12th 2010 11:14 AM baltar Kinematics and Dynamics 3 Oct 20th 2008 08:44 AM sensei Kinematics and Dynamics 3 Aug 31st 2008 10:13 AM