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On a one lane road, a person driving a car at v1=59mi/h suddenly notices a truck a distance d= 8.5 m in front of him. Th

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On a one lane road, a person driving a car at v1=59mi/h suddenly notices a truck a distance d= 8.5 m in front of him. Th

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On a one lane road, a person driving a car at v1=59mi/h
suddenly notices a truck a distance d= 8.5 m in
front of him. That truck is moving in the same direction at a
constant velocity of v2=45mi/h. In order to avoid a
collision, the person in the car has to reduce their speed to
v2 in a time interval Δt. By slamming on their
brakes, the driver can give the car a maximum negative acceleration
of ax. Assume the acceleration is constant and
that the direction of motion of the car is the positive direction,
so the acceleration ax<0.
a) Assuming the driver just barely avoids a collision, what is
the final distance, in meters, between the car and the truck?
b) Enter an expression for the distance Δx2
traveled by the truck in the time Δt, in terms of the
quantities defined in the problem statement.
c) Find an expression for the distance Δx1
traveled by the car in the time Δt, assuming the driver
brakes as hard as they can.
d) Relate the total distance the car travels
Δx1 to the distance the truck travels and the
initial distance between them.
e) Find the acceleration of the car in terms of its initial
velocity,v1, its final velocity, v2, and the time
interval Δt.
f) Use your results from (b) through (e) to find a symbolic
expression for the time Δt in terms of v1,
v2 and d.
g) Calculate the numerical value of Δt in seconds.
h) Using your result from (f), find a symbolic expression for
the acceleration ax.
i) Calculate the numerical value of ax, in
meters per second squared.
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