Moving uniformly accelerated, the car drove 1 km. The initial speed of the car is 40 km / h

Moving uniformly accelerated, the car drove 1 km. The initial speed of the car is 40 km / h, and the final speed is 80 km / h. How long did the movement last?

Data: S (the path that the car traveled while moving at uniform acceleration) = 1 km; V1 (initial vehicle speed) = 40 km / h; V2 (final speed) = 80 km / h.

We express the duration of the car’s movement from the formula: S = (V2 ^ 2 – V1 ^ 2) / 2a = S = (V2 ^ 2 – V1 ^ 2) / (2 * (V2 – V1) / t) = (V2 ^ 2 – V1 ^ 2) * t / (2 * (V2 – V1)), whence t = 2 * (V2 – V1) * S / (V2 ^ 2 – V1 ^ 2) or t = 2S / (V2 + V1).

Let’s perform the calculation: t = 2 * (80 – 40) * 1 / (80 ^ 2 – 40 ^ 2) = 0.0167 h = 1 minute.

Check: t = 2 * 1 / (80 + 40) = 1 min.