A car traveling in a straight line has a velocity
of +5.5 m/s. After an acceleration of 0.65
m/s^2 , the car’s velocity is +8.9 m/s.
In what time interval did the acceleration
occur?
Answer in units of s
Well, with an acceleration of 0.65 m/s^2, it seems like the car really couldn't decide whether it wanted to speed up or slow down. It must have been quite indecisive!
To find the time interval in which this indecisiveness occurred, we can use a simple equation of motion:
v = u + at
Where:
v = final velocity (8.9 m/s)
u = initial velocity (5.5 m/s)
a = acceleration (0.65 m/s^2)
t = time interval
Solving for t, we get:
t = (v - u) / a
Plugging in the given values:
t = (8.9 - 5.5) / 0.65
Calculating this, we find that the time interval in which the acceleration occurred is approximately 5.23 seconds.
So, in those 5.23 seconds, the car gave its best performance in the theater of motion by accelerating from 5.5 m/s to 8.9 m/s. Quite a show!
To find the time interval in which the acceleration occurred, we can use the equation:
v = u + at
Where:
v = final velocity (8.9 m/s)
u = initial velocity (5.5 m/s)
a = acceleration (0.65 m/s^2)
t = time interval
Rearranging the equation to solve for time (t):
t = (v - u) / a
Substituting the given values:
t = (8.9 - 5.5) / 0.65
t = 5.401923076923077
Rounding to the appropriate number of significant figures, the time interval in which the acceleration occurred is approximately 5.4 seconds.
To determine the time interval during which the acceleration occurred, we can use the equation:
\[ v = u + at \]
where:
- \(v\) is the final velocity \((8.9 \, \text{m/s})\),
- \(u\) is the initial velocity \((5.5 \, \text{m/s})\),
- \(a\) is the acceleration \((0.65 \, \text{m/s}^2)\), and
- \(t\) is the time interval.
Rearranging the equation to solve for \(t\), we have:
\[ t = \frac{{v - u}}{{a}} \]
Substituting the given values, we get:
\[ t = \frac{{8.9 \, \text{m/s} - 5.5 \, \text{m/s}}}{{0.65 \, \text{m/s}^2}} \]
Calculating this expression gives us:
\[ t = \frac{{3.4 \, \text{m/s}}}{{0.65 \, \text{m/s}^2}} \]
Thus, the time interval during which the acceleration occurred is approximately:
\[ t \approx 5.23 \, \text{s} \]
Therefore, the acceleration occurred over a time interval of approximately \(5.23\) seconds.