Units Dimensions and Conversions

Car companies often boast about the short time it takes their car to accelerate from 0 mph to 60 mph. If a car has a 0-to-60 time of 8.20 seconds, what is its acceleration in m/s/s?

Solution: 3.27 ms^-2

Sketch:

This problem has a slight hitch to it: We are given a speed (mph -- look at the units!) and need an acceleration -- which needs speed / time units.

So, what is the acceleration?

(change in speed) / time = (60mph - 0mph) / 8.20 s

                         = (60 mi/hr) / 8.20 s    

                         = 7.317073171 mi/hr/s

So we need to change the mi to m and the hr to s using

1 mile = 1.61x10³ meters

1 hour = 3600 seconds

So:

We'll use 3 sig figs (assuming that 0 and 60 are very accurate).

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Another Problem 2

Question:

Solution: 3.27 ms-2 Sketch:

Solution: 3.27 ms^-2

Sketch: