So lets do a little math.
Step 1
Multiply the speed in MPH by 5,280 feet per mile. The result is the speed in feet per hour. For example, 55 MPH is 290,400 feet per hour.
Step 2
Divide the speed in feet per hour by 3,600 seconds per hour. The result is the speed in feet per second. For example, 290,400 feet per hour is 80.667 feet per second.
Step 3
Alternatively, for a quick and dirty estimate, adding 50 percent is close enough (accurate to better than 2.5 percent).
Step 4
To convert feet per second into MPH, multiply by 3,600 seconds/hour and divide by 5,280 feet/mile. For example, 50 feet per second equals 34.09 MPH. Alternatively, simply divide the speed in feet per second by 1.4667 (seconds*feet)/(hours*miles). For a quick estimate, take off one third and you'll arrive at an answer accurate to better than 2.5 percent.
So if Mickey is doing 120mph at the end of the quarter, he is moving at a rate of 180 feet per second which would give him about 4.0 seconds of acceleration to the half mile.
Lets say by this time, his mph is 135. At 135, he is moving at 202.5 feet per second. This would give him about 5 seconds of acceleration to the 3/4 mile mark.
Now, lets figure at the 3/4 mile mark, his mph is 147. He is moving at 220.5 feet per second. This would give him about another 5 seconds to cover the remaining distance. Based on this theoretical calculation, his MPH at the end of the mile should be somewhere between 153 to 155.
Things to be taken into considertion: rate of acceleration, aerodynamics, road surface resistance, wind speed and direction, temperature and altitude.
In any event, I hope Mickey breaks his 160 mark. Good luck my friend!