While driving a sports car 20 m/s down a four-lane highway, a driver comes up behind a slow-moving dump truck and decides to pass it in the left-hand lane. If the driver can accelerate at 5 m/s2, how long will it take for him to reach a speed of 40 m/s?
he gains 5m/s every second
So, how long to gain 20 m/s?
(40-20)m/s / 5m/s^2 = 4s
To find the time it will take for the driver to reach a speed of 40 m/s, we can use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
We know the initial velocity is 20 m/s, and the final velocity is 40 m/s. The acceleration is given as 5 m/s².
Substituting the values into the formula, we have:
5 m/s² = (40 m/s - 20 m/s) / time
Simplifying the equation, we have:
5 m/s² = 20 m/s / time
To isolate the time, we can rearrange the equation as:
time = 20 m/s / 5 m/s²
Simplifying further, we have:
time = 4 seconds
Therefore, it will take the driver 4 seconds to reach a speed of 40 m/s.
To find out how long it will take for the driver to reach a speed of 40 m/s, we can use the equation:
vf = vo + at
Where:
- vf is the final velocity (40 m/s),
- vo is the initial velocity (20 m/s),
- a is the acceleration (5 m/s^2), and
- t is the time we need to find.
Rearranging the equation to solve for t, we get:
t = (vf - vo) / a
Plugging in the given values, we have:
t = (40 m/s - 20 m/s) / 5 m/s^2
Simplifying:
t = 20 m/s / 5 m/s^2
t = 4 seconds
Therefore, it will take the driver 4 seconds to reach a speed of 40 m/s.