a car traveling 7.0 m/s accelerates uniformly at 2.5 m/s squared to reach a speed of 12 m/s. how long does it take for the acceleration to occur?
vf=vi+at solve for t
To find the time it takes for the acceleration to occur, we can use the formula:
\(v = u + at\)
where:
\(v\) is the final velocity,
\(u\) is the initial velocity,
\(a\) is the acceleration, and
\(t\) is the time taken.
In this case, the car's initial velocity (\(u\)) is 7.0 m/s, the acceleration (\(a\)) is 2.5 m/s², and the final velocity (\(v\)) is 12 m/s. We need to find the time (\(t\)).
Rearranging the formula, we get:
\(t = \frac{{v - u}}{{a}}\)
Now we can substitute the values into the formula:
\(t = \frac{{12 - 7.0}}{{2.5}}\)
Calculating the expression, we find:
\(t = \frac{{5.0}}{{2.5}} = 2.0\) seconds
Therefore, it takes 2.0 seconds for the acceleration to occur.