Problem (1) Two cars,

A

and

B

, enter a turn simultaneously by crossing the line

C-C

. The road in this region is perfectly horizontal. At the instant the cars enter the turn,

CarA

has a speed of

50mph

and is decelerating at a constant rate of

2f(t)/(s^(2))

, and

CarB

has a speed of

50mph

and is accelerating at a constant rate of

2f(t)/(s^(2))

. Assume the cars do not drift from their lane during their turn, and that each car maintains a constant speed after exiting the turn.\ (a) Write the magnitudes of velocities and accelerations of both cars, in

f(t)/(s)

and

f(t)/(s^(2))

, respectively,\ i. halfway around the turn, and\ ii. the moment each car exits the turn.\ (b) Write the displacement functions of both cars,

\\\\Delta s(t)

, while making the turn as functions of time.\ (c) Calculate how long each car will take to complete the turn (i.e., arrive at the line

C-C

).\ (d) When the first car completes its turn, calculate the distance the second car still needs to travel to complete the turn.

Problem (1) Two cars, A and B, enter a turn simultaneously by crossing the line CC. The road in this region is perfectly horizontal. At the instant the cars enter the turn, CarA has a speed of 50mph and is decelerating at a constant rate of 2ft/s2, and Car B has a speed of 50mph and is accelerating at a constant rate of 2ft/s2. Assume the cars do not drift from their lane during their turn, and that each car maintains a constant speed after exiting the turn. (a) Write the magnitudes of velocities and accelerations of both cars, in ft/s and ft/s2, respectively, i. halfway around the turn, and ii. the moment each car exits the turn. (b) Write the displacement functions of both cars, s(t), while making the turn as functions of time. (c) Calculate how long each car will take to complete the turn (i.e., arrive at the line CC ). (d) When the first car completes its turn, calculate the distance the second car still needs to travel to complete the turn