Question

A car cruises along a winding road 100 feet behind a slow moving tractor. The travel together at 30mph until they reach an empty straight away. Passing, the car accelerates at 25ft/sec^2 until it is 100 ft ahead of the tractor.

a. Using the tractors position when the passing begins as reference, write expressions for the car and tractors positions as functions of time.

b. Combine the two functions to obtain the relative position of the car with respect to the tractor as a function of time.

c. Ignoring the lengths of the car and tractor, how many seconds does the passing maneuver take?

d. What is the car's maximum speed in MPH?

e. How long must the straightway be to safely pass?

Answer 1

At instance t = T_1 starting from t = 0 when car is behind tracks by 100 squareroot 7 distance travelled by car = distance travelled by tracks + 100 squareroot 7 Therefore 44 * T_1 + 1/2 a T^2_1 = 44 * T_1+100 rightdoublearrow 1/2*25*T^2_1 = 100 rightdoublearrow T_1 = squareroot 200/25 = squareroot 8 sex T_1 = 2.828 sec V_1 = u_1+aT_1 = 44 + 25 * squareroot 8 V_1= 114.71 m/s (velocity of car at t = T_1) Therefore Now, we take T_1 as the refrence position at t = 0 now. For any time t, car position = (114.71)t+1/ 2 times 25 times t^2 S_car = 114.71 t + 12.5 t^2 Tracker position S_track = 44 t b) Relative position of car with respect to trucker S_relative = S_Car - S_trucker = 114.71 t +12.5 t^2 - 44 t S_Relative = 70.7 t +12.5 t^2 [car is ahead of tracker] c) passing moments time T_1, as shown above = 2.828 seconds. D) Max speed of car \r\n