When at a speed of 5 m / s a car with a mass of 1 ton began to increase its speed, at this time a force 2 multiplied

When at a speed of 5 m / s a car with a mass of 1 ton began to increase its speed, at this time a force 2 multiplied by 10 to the 3rd power acts on it. How long will it take to cover 986 meters?

Data: Vm0 – machine speed before acceleration (Vm0 = 5 m / s); mm – machine weight (mm = 1 t = 103 kg); F – force acting during acceleration (F = 2 * 10 ^ 3 N); S – machine path (S = 986 m).

1) Vehicle acceleration: a = F / mm = 2 * 10 ^ 3/10 ^ 3 = 2 m / s2.

2) Machine path: S = Vm0 * t + 0.5 * a * t ^ 2.

3) Quadratic equation: 0.5 * a * t ^ 2 + Vm0 * t – S = 0.

0.5 * 2 * t ^ 2 + 5 * t – 986 = 0.

t ^ 2 + 5t – 986 = 0.

D = 52 – 4 * 1 * (-986) = 3969.

√D = 63.

4) Acceleration time: t1 = (-5 + 63) / (2 * 1) = 29 s (correct); t2 = (-5 – 63) / (2 * 1) = -34 s (wrong).

Answer: When accelerating, the car will travel 986 m in 29 s.