Question 34 of 308

A scooter accelerates from rest for time ${t}_{1}$ at constant rate ${a}_{1}$ and then retards at constant rate ${a}_{2}$ for time ${t}_{2}$ and comes to rest. The correct value of $\dfrac{{t}_{1}}{{t}_{2}}$ will be :

A$\dfrac{{a}_{2}}{{a}_{1}}$B$\dfrac{{a}_{1}}{{a}_{2}}$C$\dfrac{{a}_{1}+{a}_{2}}{{a}_{1}}$D$\dfrac{{a}_{1}+{a}_{2}}{{a}_{2}}$

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Answer: (A) $\dfrac{{a}_{2}}{{a}_{1}}$

Draw $vt$ curve

$\tan {\theta }_{1}={a}_{1}=\dfrac{{v}_{\max }}{{t}_{1}}$
&\tan {\theta }_{2}={a}_{2}=\dfrac{{v}_{\max }}{{t}_{2}}
$÷$ above
$\dfrac{{t}_{1}}{{t}_{2}}=\dfrac{{a}_{2}}{{a}_{1}}$