Problem 2. A driver traveling on a roadway decides to overtake a slow-moving tru

Question

Problem 2. A driver traveling on a roadway decides to overtake a slow-moving truck traveling at 15 mph. The accelerating characteristic of the car is given by the following: dv/dt= 2.08-0.032v where v is the speed (ft/sec), and t is the time (sec). (a) What is the acceleration of the car after 3, 7, 10, and 100 seconds? (b) What is the maximum speed attainable by the car? (c) How far will the car travel in 120 seconds? Problem 3. The driver in problem 2 stops at an intersection with a two-way stop sign. Assume that the width of the intersection in 24 ft and the car is 20 ft long. If the driver

Explanation / Answer

(a)A driver traveling on a roadway decides to overtake a slow-moving truck traveling at 15 mph

given u=15mph=22ft/sec,

dv/dt=2.08-.032v, dv/(2.08-.032v)=dt,

integrating and simplifying, v=65-31.25xe^(-.032t)

, now, put t=3,7,10,100 get corresponding values of v in ft/sec,

V3=36ft/sec, v7=40.02ft/sec, v10=42.3ft/sec, v100=63.72ft/sec,

(b)

for max speed,

a =0, dv/dt =0, 2.08-.032v=0, v(max.)=65ft/sec

(c)

from (a), we can write, ds/dt=65 - 31.25xe^(-.032t), integrating we get, s = 65t + 976.6e^(-.032t), for t=120sec, s=7826 ft

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