A motorcyclist changes the velocity of his bike from 20.0 meters/second to 35.0 meters/second under a constant acceleration of 4.00 meters/second2. How long does it take the bike to reach the final velocity?
((35.0-20.0) m/s) / (4.00 m/s^2) = 3.75s
3.75
To find the time it takes for the bike to reach the final velocity, we can use the following equation:
vf = vi + at
Where:
vf = final velocity = 35.0 m/s
vi = initial velocity = 20.0 m/s
a = acceleration = 4.00 m/s^2
t = time (unknown)
Rearranging the equation to solve for t, we have:
t = (vf - vi) / a
Plugging in the given values:
t = (35.0 m/s - 20.0 m/s) / 4.00 m/s^2
Simplifying:
t = 15.0 m/s / 4.00 m/s^2
t = 3.75 s
Therefore, it takes the bike 3.75 seconds to reach the final velocity.
To find the time it takes for the bike to reach the final velocity, we can use the equation:
\(v = u + at\)
Where:
- \(v\) is the final velocity (35.0 m/s)
- \(u\) is the initial velocity (20.0 m/s)
- \(a\) is the acceleration (4.00 m/s²)
- \(t\) is the time taken to reach the final velocity (unknown)
Rearranging the equation to solve for \(t\), we get:
\(t = \frac{{v - u}}{{a}}\)
Substituting the given values into the equation:
\(t = \frac{{35.0 \, \text{m/s} - 20.0 \, \text{m/s}}}{{4.00 \, \text{m/s²}}}\)
Calculating:
\(t = \frac{{15.0 \, \text{m/s}}}{{4.00 \, \text{m/s²}}}\)
\(t = 3.75 \, \text{s}\)
Therefore, it takes the bike 3.75 seconds to reach the final velocity of 35.0 m/s.