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Relative Motion in 1D

a car travels...

Question

a car travels first half of a length in s with velocity v₁. the second half of the length is covered with velocities v₂ and v₃ for equal time intervals.find the average velocity of the motion.

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Solution

$t o t a l d i s \tan c e = s f i r s t h a l f i s t r a v e l l e d w i t h v e l o c i t y v_{1} i n t m e t_{1} v_{1} = \frac{s / 2}{t_{1}} t_{1} = \frac{s}{2 v_{1}} s e c o n g h a l f i s t r a v e l l e d w i t h v_{2} a n d v_{3} i n e q u l a t i m e s a y t . v_{2} = \frac{s_{2}}{t} v_{3} = \frac{s_{3}}{t} s_{2} + s_{3} = \frac{s}{2} v_{2} t + v_{3} t = \frac{s}{2} (v_{2} + v_{3}) t = \frac{s}{2} t = \frac{s}{2 (v_{2} + v_{3})} a v e r a g e v e l o c i t y = \frac{n e t d i s p l a c e m e n t}{t o t a l t i m e} V = \frac{s}{t_{1} + t + t} V = \frac{s}{\frac{s}{2 v_{1}} + 2 \frac{s}{2 (v_{2} + v_{3})}} V = \frac{2 v_{1} (v_{2} + v_{3})}{2 v_{1} + v_{2} + v_{3}}$

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Relative Motion in 1D

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