Acertain car is capable of accelerating at a rate of 10.60m/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/hr

Use the equation:
v = u + at
because it has all the variables given and need to find. First you must make sure units are the same. Acceleration is given in m/s^2. Check to make sure this is correct before using the following solution. Convert acceleration from meters per second squared to miles per hour squared.

look up conversion meters to miles
1 mile = 1609.34 meters
10.60 m/s^2 * 1mile/1609.34m = 0.0069 mi/s^2
there are 3600 seconds in an hour, then there are 3600s*3600s in 1 hr^2
0.0069 mi/s^2 * 3600s*3600s/hr^2 = 85362 mi/hr^2

Then using: v = u +at
60 = 55 + 85362t
60 - 55 = 85362t
5 = 85362t
5/85362 = t
5.9 x 10^-5 hr = t
very small value in hours, multiply by 3600 to convert to seconds.

5.9 x 10^-5 hr * 3600s/hr = 0.21 seconds

26.4 is about the right time