A certain car is capable of accelerating at a rate of +0.50 m/s2. How long does it take for this car to go from a speed of 45 mi/h to a speed of 85 mi/h?
acceleration= (final velocity - initial velocity)/time
acceleration = .50 m/s^2
final velocity = 85 mi/h
initial velocity = 45 mi/h
be sure to convert mi/h to m/s!
80
To find how long it takes for the car to accelerate from 45 mi/h to 85 mi/h, we need to convert the speeds to meters per second (m/s).
First, let's convert 45 mi/h to m/s:
1 mile = 1609.34 meters
1 hour = 3600 seconds
45 mi/h * (1609.34 meters/1 mile) * (1 hour/3600 seconds) ≈ 20.11 m/s
Next, let's convert 85 mi/h to m/s:
85 mi/h * (1609.34 meters/1 mile) * (1 hour/3600 seconds) ≈ 37.98 m/s
Now that we have the initial and final speeds in m/s, we can use the acceleration formula to find the time it takes to go from 45 m/s to 85 m/s.
The acceleration formula is:
vf = vi + at
where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.
Let's rearrange the formula to solve for time (t):
t = (vf - vi) / a
Plugging in the values:
t = (37.98 m/s - 20.11 m/s) / 0.50 m/s^2
First, subtract the initial velocity from the final velocity:
t = 17.87 m/s / 0.50 m/s^2
Then, divide the result by the acceleration:
t ≈ 35.74 seconds
Therefore, it takes approximately 35.74 seconds for the car to go from a speed of 45 mi/h to a speed of 85 mi/h.