A car with a mass of 1 t accelerates from rest to a speed of 20 m / s. What is the acceleration time of the car

A car with a mass of 1 t accelerates from rest to a speed of 20 m / s. What is the acceleration time of the car if it is affected by a traction force of 2 kN and a resistance force of 1 kN?

m = 1 t = 1000 kg.

V0 = 0 m / s.

V = 20 m / s.

Ft = 2 kN = 2000 N.

Fcopr = 1 kN = 1000 N.

t -?

The acceleration time of the car t is expressed from the formula for acceleration: a = (V – V0) / t.

t = (V – V0) / a.

The acceleration of the car a is directly proportional to the resultant of all forces Fр that act on it, and is inversely proportional to the mass of the car m: a = Fр / m.

The vector resultant force Fr is expressed by the sum: Fr = Ft + Fcopr.

Since the resistance force is always directed in the opposite direction of the movement of the body and the traction force, then for projections Fр = Fт – Fсopr.

t = (V – V0) * m / (Fт – Fcopr).

t = (20 m / s – 0 m / s) * 1000 kg / (2000 N – 1000 N) = 20 s.

Answer: car acceleration lasts t = 20 s.