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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?\\n

Commented byTawa11 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 byTawa11 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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