With what acceleration and how long did the car move if on the way of 10 km its speed increased

With what acceleration and how long did the car move if on the way of 10 km its speed increased from 36 km / h to 72 km / h?

Problem data: S (the path taken by the given car) = 10 km = 10 * 10 ^ 3 m; V0 (initial speed) = 36 km / h = 10 m / s; V (speed after acceleration) = 72 km / h = 20 m / s.

1) Vehicle acceleration: S = (V2 – V0 ^ 2) / 2a, whence we express: a = (V2 – V0 ^ 2) / 2S = (20 ^ 2 – 10 ^ 2) / (2 * 10 * 10 ^ 3 ) = 0.015 m / s2.

2) Time of movement: t = (V – V0) / a = (20 – 10) / 0.015 = 666.7 s = 11.1 minutes.

Check: S = V0 * t + a * t ^ 2/2 = 10 * 666.7 + 0.015 * 666.7 ^ 2/2 = 10 * 10 ^ 3 km (correct).