Question

Мотоциклист и велосипедист одновременно начинают равноускоренное движение из состояния покоя.Ускорение мотоциклиста в 3 раза больше, чем ускорение велосипедиста.Во сколько раз больше времени понадобится велосипедисту, чтобы достичь скорости 50 км/ч?

Answer 1

V = a·tв ⇒ tв = $\frac{v}{a}$
v = 3a·tм ⇒ tм = $\frac{v}{3a}$
tв/tм = $\frac{\frac{v}{a}}{\frac{v}{3a}}$ = $\frac{3av}{av}$ = 3

Answer 2

Problem Analysis

We are given that a motorcyclist and a cyclist start moving from rest with the same constant acceleration. The acceleration of the motorcyclist is three times greater than the acceleration of the cyclist. We need to determine the ratio of the time it takes for the cyclist to reach a speed of 50 km/h compared to the motorcyclist.

Solution

Let's assume the acceleration of the cyclist is a and the acceleration of the motorcyclist is 3a. We need to find the ratio of the time it takes for the cyclist to reach a speed of 50 km/h compared to the motorcyclist.

To solve this problem, we can use the equations of motion. The equation that relates acceleration, initial velocity, final velocity, and time is:

v = u + at

where: - v is the final velocity - u is the initial velocity - a is the acceleration - t is the time

For the cyclist: - Initial velocity, u_cyclist = 0 (since the cyclist starts from rest) - Final velocity, v_cyclist = 50 km/h = 50 * (1000/3600) m/s (converting km/h to m/s) - Acceleration, a_cyclist = a

For the motorcyclist: - Initial velocity, u_motorcyclist = 0 (since the motorcyclist starts from rest) - Final velocity, v_motorcyclist = 50 km/h = 50 * (1000/3600) m/s (converting km/h to m/s) - Acceleration, a_motorcyclist = 3a

We can rearrange the equation to solve for time:

t = (v - u) / a

For the cyclist: t_cyclist = (v_cyclist - u_cyclist) / a_cyclist

For the motorcyclist: t_motorcyclist = (v_motorcyclist - u_motorcyclist) / a_motorcyclist

To find the ratio of the time it takes for the cyclist to reach a speed of 50 km/h compared to the motorcyclist, we can divide the two equations:

ratio = t_cyclist / t_motorcyclist

Let's calculate the values and find the ratio.

Calculation

Given: - Final velocity, v_cyclist = 50 * (1000/3600) m/s - Final velocity, v_motorcyclist = 50 * (1000/3600) m/s - Acceleration, a_motorcyclist = 3a

Using the equations: t_cyclist = (v_cyclist - u_cyclist) / a_cyclist t_motorcyclist = (v_motorcyclist - u_motorcyclist) / a_motorcyclist

Substituting the values: t_cyclist = (50 * (1000/3600) - 0) / a t_motorcyclist = (50 * (1000/3600) - 0) / (3a)

Simplifying: t_cyclist = (50 * (1000/3600)) / a t_motorcyclist = (50 * (1000/3600)) / (3a)

Calculating the ratio: ratio = t_cyclist / t_motorcyclist = [(50 * (1000/3600)) / a] / [(50 * (1000/3600)) / (3a)]

Simplifying: ratio = 3

Answer

The ratio of the time it takes for the cyclist to reach a speed of 50 km/h compared to the motorcyclist is 3.

Explanation

The cyclist takes three times longer to reach a speed of 50 km/h compared to the motorcyclist. This is because the motorcyclist has three times the acceleration of the cyclist, allowing them to reach the desired speed in a shorter amount of time.