A certain car is capable of accelerating at a rate of + 0.30 m/s2. How long does it take for this car to go from a speed of 55 mi/h to a speed of 80 mi/h?
Vf - Vo = 80 - 55 = 25mi/h.
25mi/h * 1600m/mi * (1/3600h/s =11.11m/s.
a = (Vf - Vo) / t = 0.30m/s^2,
(11.11) / t = 0.30,
0.3t = 11.11,
t = 37s.
To solve this problem, we need to convert the speeds from miles per hour (mi/h) to meters per second (m/s) and then find the time needed for the acceleration.
Step 1: Convert speed from miles per hour to meters per second.
We know that 1 mile = 1609.34 meters and 1 hour = 3600 seconds.
So, to convert 55 mi/h to m/s, we can use the following conversion factor:
55 mi/h * (1609.34 meters/1 mile) * (1 hour/3600 seconds) = 24.59 m/s
Similarly, converting 80 mi/h to m/s:
80 mi/h * (1609.34 meters/1 mile) * (1 hour/3600 seconds) = 35.76 m/s
Step 2: Calculate the time needed for acceleration.
We can use the equation:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Since the car starts from rest (initial velocity = 0 m/s), the equation becomes:
v = at
Here, the initial velocity is 24.59 m/s (from Step 1), the final velocity is 35.76 m/s (from Step 1), and the acceleration is +0.30 m/s².
Substituting the values into the equation, we have:
35.76 m/s = 0.30 m/s² * t
Step 3: Solve for time (t).
Divide both sides of the equation by 0.30 m/s²:
t = 35.76 m/s / 0.30 m/s²
Calculating the time:
t = 119.2 seconds
Therefore, it will take approximately 119.2 seconds for the car to go from a speed of 55 mi/h to a speed of 80 mi/h.
To find the time it takes for the car to go from a speed of 55 mi/h to a speed of 80 mi/h, we need to use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
Since the car is accelerating at +0.30 m/s^2, we need to convert the given speeds from miles per hour to meters per second.
1 mile = 1609.34 meters
1 hour = 3600 seconds
Initial velocity = 55 mi/h = (55 * 1609.34 m) / 3600 s ≈ 24.59 m/s
Final velocity = 80 mi/h = (80 * 1609.34 m) / 3600 s ≈ 35.76 m/s
Now we can plug these values into the formula and solve for time:
0.30 m/s^2 = (35.76 m/s - 24.59 m/s) / time
To solve for time, we rearrange the formula:
time = (final velocity - initial velocity) / acceleration
time = (35.76 m/s - 24.59 m/s) / 0.30 m/s^2
Calculating the value:
time = 11.17 s
Therefore, it takes approximately 11.17 seconds for the car to go from a speed of 55 mi/h to a speed of 80 mi/h.