you travel at 60 mph for 3 minutes. Then, you speed up to 80 mph which took 200 meters. Finally, you come to a stop which took 1 mile.

Question

1. how much time did this take?
2. how far did you travel?

Answer 1

1st part

1 mile is 1.609 km. In 3 minutes you travel (3/60) x 60 = 3 miles = 4.827 km = 4827 m

So first part : time 180 s, distance 4.827 km

60 mph = 60 x 1.609 x 1000 / 3600 m/s = 26.8 m/s

80 mph = 80 x 1.609 x 1000 /3600 m/s = 35.8 m/s

So second part : distance = 200 m

Time : v^2 = u^2 + 2as, v = 35.8, u = 26.8, s = 200, giving a = 1.4085 m/s/s

v = u+at giving t = (35.8 - 26.8) / 1.4085 = 6.39 s

Third part. Stop in 1 mile. Distance = 1.609 km = 1609 m

v^2 = u^2 + 2as, v = 0, u = 35.8, s = 1609 giving a = -0.3983 m/s/s

v= u + at, so t = 35.8 / 0.3983 = 89.88 s

So to conclude

1 2 3 TOTAL

Distance 4827 200 1609 6636 m

Time 180 6.39 89.88 276.27 s