A225 kg red bumper car is moving at 3.0 m/s. it hits a stationary 180kg blue bumper car. the red and blue bumped cars combine and hit a stationary green bumper car of mass 150kg. the red, blue and green bumper cars all combine. what is the final velocity of the combined bumper cars?

1.22 m/s

Explanation:

By using the conservation of momentum of red and blue car

225 x 3 + 180 x 0 = (225 + 180) v

Where, v be the speed of blue and red car combined together.

675 = 405 v

v = 1.667 m /s

now the conservation of momentum for blue red combination and green car

(225 + 180) x 1.667 = (225 + 180 + 150) v'

Where v' is the speed of combined cars

675 = 555 v'

v' = 1.22 m/s

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

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