Question

a car accelerates uniformly from rest to a speed of 65 km/h (18 m/s) in 12s. Find the distance the car travels during this time?

Answer 1

The car's speed was zero at the beginning of the 12 seconds,
and 18 m/s at the end of it.  Since the acceleration was 'uniform'
during that time, the car's average speed was (1/2)(0 + 18) = 9 m/s.

12 seconds at an average speed of 9 m/s  ==>  (12 x 9) = 108 meters .

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That's the way I like to brain it out.  If you prefer to use the formula,
the first problem you run into is:  You need to remember the formula !

The formula is        D = 1/2 a T²

                   Distance = (1/2 acceleration) x (time in seconds)²

             Acceleration = (change in speed) / (time for the change)
                                  =        (18 m/s)            /        (12 sec)
                                  =                      1.5 m/s² .

                  Distance  =  (1/2 x 1.5 m/s²) x (12 sec)²
                                  =       (0.75 m/s²)  x  (144 sec²)  =  108 meters .