A-particle-is-moving-along-a-straight-line-with-uniform-acceleration-has-velocities-7-m-s-at-P-and-17-m-s-at-Q-If-R-is-the-midpoint-of-PQ-then-the-average-velocity-between-P-and-R-is-

Question Number 15856 by Tinkutara last updated on 14/Jun/17

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{along}\:\mathrm{a}\:\mathrm{straight} \\ $$$$\mathrm{line}\:\mathrm{with}\:\mathrm{uniform}\:\mathrm{acceleration}\:\mathrm{has} \\ $$$$\mathrm{velocities}\:\mathrm{7}\:\mathrm{m}/\mathrm{s}\:\mathrm{at}\:{P}\:\mathrm{and}\:\mathrm{17}\:\mathrm{m}/\mathrm{s}\:\mathrm{at}\:{Q}. \\ $$$$\mathrm{If}\:{R}\:\mathrm{is}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of}\:{PQ},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{average}\:\mathrm{velocity}\:\mathrm{between}\:{P}\:\mathrm{and}\:{R}\:\mathrm{is}? \\ $$

Answered by ajfour last updated on 14/Jun/17

$$\left({v}_{{PR}} \right)_{{avg}} =\frac{{v}_{{P}} }{\mathrm{2}}\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\sqrt{\mathrm{1}+\frac{{v}_{{Q}} ^{\mathrm{2}} }{{v}_{{P}} ^{\mathrm{2}} }}\:\right)\:. \\ $$

Commented by Tinkutara last updated on 14/Jun/17

$$\mathrm{Can}\:\mathrm{you}\:\mathrm{tell}\:\mathrm{the}\:\mathrm{final}\:\mathrm{answer}\:\mathrm{please}? \\ $$

Commented by ajfour last updated on 14/Jun/17

$$\:\:\:\mathrm{10}{m}/{s}\:. \\ $$

Commented by Tinkutara last updated on 14/Jun/17

$$\mathrm{Do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{that}\:\mathrm{for}\:\mathrm{calculating}\:\mathrm{this}, \\ $$$$\mathrm{the}\:\mathrm{formula}\:\mathrm{is}\:{v}_{\mathrm{av}} \:\mathrm{between}\:{P}\:\mathrm{and}\:{R}\:= \\ $$$$\frac{{v}_{{P}} \:+\:{v}_{{R}} }{\mathrm{2}}\:?\:\mathrm{I}\:\mathrm{have}\:\mathrm{calculated}\:{v}_{{R}} . \\ $$

Commented by ajfour last updated on 14/Jun/17

$${v}_{{R}} =\sqrt{\frac{{v}_{{P}} ^{\mathrm{2}} +{v}_{{Q}} ^{\mathrm{2}} }{\mathrm{2}}}\:\:\:=\mathrm{13}{m}/{s}\:. \\ $$

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