Two Cars Start from Rest at a Traffic Light $v _ { 1 } ( t ) = \frac { 1 } { 2 } t$

Essay

Two cars start from rest at a traffic light. Car 1 travels at a speed given by $v _ { 1 } ( t ) = \frac { 1 } { 2 } t$ feet
per minute, and Car 2 travels at a speed given by $v _ { 2 } ( t ) = \frac { 1 } { 4 } t ^ { 2 },$ feet per minute.(a) Which car is ahead after 2 minutes? Justify.(b) Which car is ahead after 3 minutes? Justify.(c) Which car is ahead after 4 minutes? Justify.(d) At what time(s) do the two cars travel at the same speed?