Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 97

Freeway entrance ramps. When freeways were first built in the United States in the 1950s, entrance ramps were often too short for an entering car to safely merge into existing traffic. Consider an aggressive car acceleration of \( a = 4.0 \text{ m/s}^2 \) and an initial car speed of \( v_0 = 25 \text{ mi/h} \) as the car enters the entrance ramp of a freeway where other cars are moving at \( 55 \text{ mi/h} \). (a) If the ramp has a length of \( d = 40 \text{ yd} \), what is the car's speed \( v \) in miles per hour as it attempts to merge? (b) What is the minimum length \( d \) in yards needed for the car's speed to match the speed of the other cars?