Determine the average speed of a car moving in a straight line, if the first half of the
Determine the average speed of a car moving in a straight line, if the first half of the journey he moved 80 km / h, and the remaining 40 km / h.
V1 = 80 km / h.
V2 = 40 km / h.
S1 = S2 = S / 2.
Vav -?
To find the average speed of movement Vav, it is necessary to divide the entire path traveled by the car S by the time of its movement t along the entire path: Vav = S / t.
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 half of the path, t2 is the time of movement on the second half of the path.
t1 = S1 / V1 = S / 2 * V1.
t2 = S2 / V2 = S / 2 * V2.
t = S / 2 * V1 + S / 2 * V2 = (S * V2 + S * V1) / 2 * V1 * V2 = S * (V2 + V1) / 2 * V1 * V2.
Vav = S * 2 * V1 * V2 / S * (V2 + V1) = 2 * V1 * V2 / (V2 + V1).
Vav = 2 * 80 km / h * 40 km / h / (40 km / h + 80 km / h) = 53.3 km / h.
Answer: the average vehicle speed was Vav = 53.3 km / h.