A car that starts from rest and has uniform acceleration. The car must travel 60 meters before reaching a speed of 10 m/s. What total distance must the car travel in order to reach a speed of 30 m/s?

Answer 1

average speed for 60 m is ... (0 + 10) / 2 = 5 m/s
... so travel time is ... 60 / 5 = 12 s
... and acceleration is ... 10 m/s / 12 s = 5/6 m/s^2

time to reach 30 m/s ... 30 / 5/6 = 36 s
... average speed is ... (0 + 30) / 2 = 15 m/s
... distance is ... 36 s * 15 m/s = 540 m

with uniform acceleration ... d = 1/2 a t^2
... the distance is proportional to the square of the time
... three times the time means nine times the distance