The initial velocity is miles/h.

The final velocity is miles/h.

The distance traveled during deceleration is ft.

Convert the velocity in feet per second.

mile/hour ft/sec.

miles/hour ft/sec.

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Find velocity function:

The car travels with a constant deceleration.

.

The rate of change in velocity is acceleration:.

.

.

The velocity at is

Substitute initial velocity .

.

The velocity .

Equate .

.

Find acceleration:

The rate of change in position is velocity: .

.

.

The distance at is,

.

.

Substitute in .

The acceleration is ft/sec/sec.

(negative because of deceleration).

(a)

Find position of car when speed reduced to miles/h.

miles/h ft/sec.

Position function .

.

Find .

Substitute and in .

Substitute in .

The position of car when speed reduced to miles/h is ft.

(b)

Find position of car when speed reduced to miles/h.

miles/h ft/sec.

Position function .

Find .

Substitute and in .

Substitute in .

The position of car when speed reduced to miles/h is ft.

Graph the real number line for distance traveled by car.

Observe from the graph:

The distance traveled per second is decreasing until it finally stops.

(a) The position of car when speed reduced to miles/h is ft.

(b) The position of car when speed reduced to miles/h is ft.

(c)

Graph the real number line for distance traveled by car.

The distance traveled per second is decreasing until it finally stops.