Thermodynamics Question

Question

A 95-slug automobile changes speed from 55 mi/h to 30 mi/h while climbing a 3° hill. If the change in speed occurs over a 1335-ft straight section of road, find the total work.

Answer: -270 ft • lbf

I just need to know the steps to solve

Answer 1

55 miles per hour translates to 80.666666666 feet per second.

30 miles per hour translates to 44 feet per second.

(44 feet per second)² = (80.666666666 feet per second)² + 2(acceleration)(1335 feet) which reduces to acceleration = -1.712026634 feet per second every second.

Then (mass)(acceleration)(distance) gives (95 slugs)(-1.712026634 feet per second every second)(1335 feet) gives work (or a force exerted through a distance) as -217127.7779 [(slug•feet²) per second²].

Note that 0.5(95 slugs)(44 feet per second)² − 0.5(95 slugs)(80.666666666 feet per second)² simplifies to -217127.7779 [(slug•feet²) per second²] as well.