A certain car is capable of accelerating at a rate of + 0.60 m/s^2. How long does it take for this car to go from a speed of 55 mi/h to a speed of 60 mi/h?

To find the answer, we need to convert the given speeds from miles per hour (mi/h) to meters per second (m/s), and then apply the equation of motion for acceleration. Here's how we can do it step by step:

Step 1: Convert speeds from miles per hour to meters per second.
Since 1 mile = 1609.34 meters and 1 hour = 3600 seconds, we can use the conversion factor of 1 mi/h = 0.447 m/s.
Thus, the initial speed is:
v1 = 55 mi/h * 0.447 m/s per mi/h = 24.6 m/s

And the final speed is:
v2 = 60 mi/h * 0.447 m/s per mi/h = 26.8 m/s

Step 2: Use the equation of motion for acceleration.
The equation of motion for acceleration is: vf = vi + at,
where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.

In this case, we know the initial speed (vi = 24.6 m/s), the final speed (vf = 26.8 m/s), and the acceleration (a = 0.60 m/s^2). We need to find the time (t).

Rearranging the equation and solving for t, we have: t = (vf - vi) / a

Substituting the known values, we have: t = (26.8 m/s - 24.6 m/s) / 0.60 m/s^2

Step 3: Calculate the time.
t = 2.2 m/s / 0.60 m/s^2

Dividing the numerator by the denominator, we get: t = 3.67 seconds

Therefore, it takes approximately 3.67 seconds for the car to go from a speed of 55 mi/h to a speed of 60 mi/h.

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