Question

Мотоциклист и велосипедист одновременно начинают движение по прямой из состояния покоя. Ускорение мотоциклиста в три раза больше, чем велосипедиста. Во сколько раз скорости мотоциклиста больше скорости велосипедиста в один и тот же момент времени?

Answer 1

Ответ:в 3 раза. По­сколь­ку и ве­ло­си­пе­дист, и мо­то­цик­лист на­чи­на­ют дви­же­ние из со­сто­я­ния покоя, за­ко­ны из­ме­не­ния их ско­ро­стей со вре­ме­нем вы­гля­дят сле­ду­ю­щим образом:Vвел(t)=Авел(t),Vмот(t)=Aмотt=3Aвелt,где A ускорение,t время.

Answer 2

Calculation of Speed Ratio between a Motorcyclist and a Cyclist

To determine the ratio of the speed of the motorcyclist to the speed of the cyclist at the same moment in time, we need to consider their respective accelerations.

Given that the acceleration of the motorcyclist is three times greater than that of the cyclist, we can establish the following relationship:

Acceleration of Motorcyclist (a_m) = 3 * Acceleration of Cyclist (a_c)

Since both the motorcyclist and the cyclist start from a state of rest, we can assume that their initial velocities are zero.

Using the equation of motion v = u + at, where: - v is the final velocity, - u is the initial velocity, - a is the acceleration, and - t is the time,

we can calculate the final velocities of the motorcyclist (v_m) and the cyclist (v_c) at the same moment in time.

For the motorcyclist: v_m = 0 + a_m * t

For the cyclist: v_c = 0 + a_c * t

Since we are interested in the ratio of their speeds, we can divide the equation for the motorcyclist's velocity by the equation for the cyclist's velocity:

v_m / v_c = (a_m * t) / (a_c * t)

The time (t) cancels out, leaving us with:

v_m / v_c = a_m / a_c

Substituting the given relationship between the accelerations, we have:

v_m / v_c = 3 / 1

Therefore, the speed of the motorcyclist is three times greater than the speed of the cyclist at the same moment in time.