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A-bicycle-has-a-constant-velocity-of-10-m-s-A-person-starts-from-rest-and-runs-to-catch-up-to-the-bicycle-in-30-s-What-is-the-acceleration-of-the-person-




Question Number 171332 by Tawa11 last updated on 12/Jun/22
A bicycle has a constant velocity of 10 m/s. A person starts from rest and runs to catch up to the bicycle in 30 s. What is the acceleration of the person?
A bicycle has a constant velocity of 10 m/s. A person starts from rest and runs to catch up to the bicycle in 30 s. What is the acceleration of the person?
Commented by Tawa11 last updated on 12/Jun/22
I work towards answer to get       300   =   450a,      a  =   (2/3) m/s^2 .  I want to know why the bicycle time too is  30sec.  Since the question did not indicate equal time.    For bicycle:  s   =  vt    =   10(30)   =   300m  For person:    s   =   (1/2)at^2    =   (1/2)  ×  a  ×  30^2    =   (1/2)  ×  a  ×  900   =   450a  Equal distance            300   =   450a
$$\mathrm{I}\:\mathrm{work}\:\mathrm{towards}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{get} \\ $$$$\:\:\:\:\:\mathrm{300}\:\:\:=\:\:\:\mathrm{450a},\:\:\:\:\:\:\mathrm{a}\:\:=\:\:\:\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} . \\ $$$$\mathrm{I}\:\mathrm{want}\:\mathrm{to}\:\mathrm{know}\:\mathrm{why}\:\mathrm{the}\:\mathrm{bicycle}\:\mathrm{time}\:\mathrm{too}\:\mathrm{is}\:\:\mathrm{30sec}. \\ $$$$\mathrm{Since}\:\mathrm{the}\:\mathrm{question}\:\mathrm{did}\:\mathrm{not}\:\mathrm{indicate}\:\mathrm{equal}\:\mathrm{time}. \\ $$$$ \\ $$$$\mathrm{For}\:\mathrm{bicycle}:\:\:\mathrm{s}\:\:\:=\:\:\mathrm{vt}\:\:\:\:=\:\:\:\mathrm{10}\left(\mathrm{30}\right)\:\:\:=\:\:\:\mathrm{300m} \\ $$$$\mathrm{For}\:\mathrm{person}:\:\:\:\:\mathrm{s}\:\:\:=\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{at}^{\mathrm{2}} \:\:\:=\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\:×\:\:\mathrm{a}\:\:×\:\:\mathrm{30}^{\mathrm{2}} \:\:\:=\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\:×\:\:\mathrm{a}\:\:×\:\:\mathrm{900}\:\:\:=\:\:\:\mathrm{450a} \\ $$$$\mathrm{Equal}\:\mathrm{distance} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{300}\:\:\:=\:\:\:\mathrm{450a} \\ $$
Commented by Tawa11 last updated on 12/Jun/22
Or the question means that they both start from the beginning.  And the person still be in the same position as the bicycle after  30 seconds?
$$\mathrm{Or}\:\mathrm{the}\:\mathrm{question}\:\mathrm{means}\:\mathrm{that}\:\mathrm{they}\:\mathrm{both}\:\mathrm{start}\:\mathrm{from}\:\mathrm{the}\:\mathrm{beginning}. \\ $$$$\mathrm{And}\:\mathrm{the}\:\mathrm{person}\:\mathrm{still}\:\mathrm{be}\:\mathrm{in}\:\mathrm{the}\:\mathrm{same}\:\mathrm{position}\:\mathrm{as}\:\mathrm{the}\:\mathrm{bicycle}\:\mathrm{after}\:\:\mathrm{30}\:\mathrm{seconds}? \\ $$

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