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) $\frac { \alpha \beta } { 4 ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$
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) $\frac { \alpha \beta } { 4 ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$