Ok, this is not too hard. 1680 miles per hour (70 mph times 24 for the scale) is 751 metres per second. To reach that speed in 0.25 seconds requires an average acceleration of 3000 m.s-2. The acceleration of gravity is 9.80665 m.s-2, say 10. So, we're talking 300 gravities here.
Getting back to your slot car, if its mass is in proportion to the linear scale of 1/24, we can expect it to weigh about 100 g. At 70 m.p.h. (31.3 m.s-1), its kinetic energy is 49 joules. To get that much energy into the car in 0.25 seconds, the mechanical output of the motor must be 200 watts. For a typical small motor, not really desiged for efficiency, the electrical input would have to be 300 to 400 watts. The average acceleration is 125 m.s-2. The force required to give this acceleration is 12.5 newtons. With only a little more than one newton (100 g force) holding the car down on the track, you need a coefficient of friction of 12.5. Are you sure the 70 m.p.h. is real-world speed and not scale speed?
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