# A scooter accelerates from rest for time

Question:

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

1. (1) $\frac{a_{1}+a_{2}}{a_{2}}$

2. (2) $\frac{a_{2}}{a_{1}}$

3. (3) $\frac{a_{1}+a_{2}}{a_{1}}$

4. (4) $\frac{a_{1}}{a_{2}}$

Correct Option: , 2

Solution:

(2)

From given information:

For $1^{\text {st }}$ interval

$a_{1}=\frac{v_{0}}{t_{1}}$

$v_{0}=a_{1} t_{1} \quad \ldots . .(1)$

For $2^{\text {nd }}$ interval

$a_{2}=\frac{v_{0}}{t_{2}}$

$v_{0}=a_{2} t_{2} \quad \ldots \ldots(2)$

from (1)\&(2)

$a_{1} t_{1}=a_{2} t 2$

$\frac{t_{1}}{t_{2}}=\frac{a_{2}}{a_{1}}$