The car traveled three quarters of the entire path at a speed of v1, and the rest of the track at a speed of v2.

The car traveled three quarters of the entire path at a speed of v1, and the rest of the track at a speed of v2. a) Express the entire time of the car’s movement through v1, v2 and the entire traversed path l. b) Express the average vehicle speed in terms of v1 and v2. c) Find the numerical value of the average speed at v1 = 80 km / h, v2 = 100 km / h.

V1 = 80 km / h.

V2 = 100 km / h.

l1 = 3 * l / 4.

t -?

Vav -?

The travel time of the entire path is expressed by the sum: t = t1 + t2, where t1 is the time of movement on the first part of the path, t2 is the time of movement on the second part of the path.

t1 = l1 / V1 = 3 * l / 4 * V1.

l2 = l – l1 = l – 3 * l / 4 = l / 4.

t2 = l2 / V2 = l / 4 * V2.

t = 3 * l / 4 * V1 + l / 4 * V2 = (3 * l * V2 + l * V1) / 4 * V1 * V2 = l * (3 * V2 + V1) / 4 * V1 * V2.

To find the average speed of movement Vav, it is necessary to divide the entire traversed path l by the time of its movement t: Vav = l / t.

Vav = l * 4 * V1 * V2 / l * (3 * V2 + V1) = 4 * V1 * V2 / (3 * V2 + V1).

Vav = 4 * 80 km / h * 100 km / h / (3 * 100 km + 80 km / h) = 84.2 km / h.

Answer: the average speed of the vehicle along the entire path was Vav = 84.2 km / h.