a car enters the freeway with a speed of 5.6 m/s and accelerates uniformly for 2.7 km in 3.0 minutes.How fast is the car moving after this time? answer in units of m/s
4.08
42
To find the final speed of the car after accelerating uniformly, we need to use the equations of motion.
First, let's convert the initial speed from m/s to km/h:
Initial speed = 5.6 m/s
Converting to km/h: 5.6 * (3600/1000) = 20.16 km/h
Next, we need to convert the distance traveled from kilometers to meters:
Distance = 2.7 km
Converting to meters: 2.7 * 1000 = 2700 m
Now, let's convert the time taken from minutes to seconds:
Time = 3.0 minutes
Converting to seconds: 3.0 * 60 = 180 s
The equation that relates final speed (vf), initial speed (vi), acceleration (a), and time (t) is:
vf = vi + a * t
Since the car is accelerating uniformly, we can assume that the acceleration is constant throughout.
We know the initial speed (vi) is 20.16 km/h = 5.6 m/s, and the time (t) is 180 s. We need to find the acceleration (a).
Using the equation and rearranging it to solve for acceleration:
a = (vf - vi) / t
Since we want to find the final speed (vf), we rearrange the equation again:
vf = vi + a * t
Now, we can substitute the known values:
vf = 5.6 m/s + a * 180 s
To find the acceleration (a), we need to use the formula for uniform acceleration:
a = (vf - vi) / t
We can rearrange this equation to solve for acceleration:
a = (vf - 5.6 m/s) / 180 s
Finally, we substitute the known values:
vf = 5.6 m/s + [(vf - 5.6 m/s) / 180 s] * 180 s
To solve this equation, we isolate the variable "vf" on one side:
vf - (vf / 180) * 180 = 5.6
Simplifying the equation:
vf - vf = 5.6
0 = 5.6
Since this equation does not have a valid solution, there seems to be an error in the given information or calculations. Please double-check the values and try again.