A body travels a distance $s$ in $t$ seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration $f$ and in the second part with constant retardation $r$. The value of $t$ is given by
(1) $\sqrt{2s\left(\frac{1}{f} + \frac{1}{r}\right)}$
(2) $2s\left(\frac{1}{f} + \frac{1}{r}\right)$
(3) $\frac{2s}{\frac{1}{f} + \frac{1}{r}}$
(4) $\sqrt{2s(f + r)}$

A car starting from rest accelerates at the rate $f$ through a distance $S$, then continues at constant speed for time $t$ and then decelerates at the rate $f/2$ to come to rest. If the total distance traversed is 15 S, then
(1) $S = ft$
(2) $\mathrm{S} = 1/6\, \mathrm{ft}^2$
(3) $\mathrm{S} = 1/2\, \mathrm{ft}^2$
(4) None of these

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 $\frac { t _ { 1 } } { t _ { 2 } }$ will be :
(1) $\frac { a _ { 2 } } { a _ { 1 } }$
(2) $\frac { a _ { 1 } } { a _ { 2 } }$
(3) $\frac { a _ { 1 } + a _ { 2 } } { a _ { 1 } }$
(4) $\frac { a _ { 1 } + a _ { 2 } } { a _ { 2 } }$

A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is t seconds, the total distance travelled is:
(1) $\frac { 4 \alpha \beta } { ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$
(2) $\frac { 2 \alpha \beta } { ( \alpha + \beta ) } t ^ { 2 }$
(3) $\frac { \alpha \beta } { 2 ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$
(4) $\frac { \alpha \beta } { 4 ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$