To me, the hardest part of this whole thing is keeping the units straight. We're starting out with information given to us in kilometers, hours, and meters, and we have to come up with answers in m/s² , seconds, and meters.
When I worked this problem, I jumped right in without thinking, and I immediately got bogged down when I had to go off to the side and convert some units.
Now I know better. THIS time, before we get all tangled up trying to solve anything, let's get clever and change everything to m/s right now !
(54 km/hour) · (1,000m/km) · (1 hour/3600 sec) = 15 meters/second
(18 km/hour) · (1,000 m/km) · (1 hour/3600 sec) = 5 meters/second
NOW I'll betcha it's gonna be about 70% faster and easier !
i). Acceleration = (change in speed / time for the change)
We know the distance, but not the time. I know there's a formula for it, but I've learned so many formulas during my lifetime that I can't remember ALL of them. So I just memorize some of them, and I work things out from the formulas that I know. Here's how I do time:)
Average speed during the given slow-down = (1/2)·(15+5) = 10 m/s
Distance covered during the given slow-down = 10 m.
Time = (distance) / (average speed) = (10m) / (10 m/s) = 1 second
Acceleration = (change in speed) / (time for the change)
Acceleration = (5 m/s - 15 m/s) / (1 second)
Acceleration = (-10 m/s) / (1 second)
Acceleration = -10 m/s² (or 'Deceleration' = 10 m/s² )
For parts ii). and iii)., there's a big shift in the question.
It only gave you the slow-down from 54 to 18 km/hr for the purpose of calculating the deceleration. NOW, for the rest of the answers, it's talking about a complete stop ... 0 m/s .
ii). Time required to stop = (initial speed) / (deceleration)
Time to stop from 54 km/hr = (15 m/s) / (10 m/s²)
Time to stop = 1.5 seconds
iii). Distance covered = (average speed) · (time to stop)
Distance covered = (7.5 m/s) · (1.5 sec)
Distance covered = 11.25 meters
OR ... use the official formula:
Distance = (1/2) · (acceleration) · (time² )
Distance = (1/2) · (10 m/s²) · (1.5 sec)²
Distance = 11.25 meters yay !
