Sam was driving with a speed of 45 miles per hour until a dog runs in front of him and suddenly he hits the brakes to decelerate his speed rapidly to 15 mph in 30s. Calculate his deceleration in m/s^2.
- We need to start by converting our units from miles per hour to meters per second.
Initial velocity:
45 miles per hour x 1609.344 meters / mile x 1 hour / 60 minutes x 1 minute / 60 seconds = 20.1168 m/s
Ending velocity:
15 miles per hour x 1609.344 meters/ mile x 1 hour / 60 minutes x 1 minute / 60 seconds = 6.7056 m/s
2. Next, we need to calculate acceleration. Please keep in mind that, in physics, we do not use the word "deceleration" or "decelerate." Any change in velocity or in direction is a form of acceleration, even if the change in velocity results in the object moving more slowly. We'll need the acceleration formula.
where v = ending velocity, v0 = initial velocity, and Δt = change in time.
Thus:
20.1168 m/s - 6.7056 m/s / 30 s = 0.44704 m/s2.
We need to adjust our answer to take account of significant figures. Since the values of each of our variables have two significant figures, we'll round our answer to 0.45 m/s2.
Next, we need to adjust the sign of our answer. Since, by convention, a reduction in velocity is denoted with a negative sign, we'll write our answer as being that acceleration is equal to -0.45 m/s2.
That is our final answer.
