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.