### 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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**Mon May 16, 2022 10:50 am**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.

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.