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?Можно пожалуйста с решением)))

Answer 1

V - скорость
A - ускорение
t - время
в. и м. - велосипедиста/мотоциклиста

Дано:
Aм=3Aв.
V=50км/ч
tв./tм. - ?

V=at
tв.=50/Aв.
tм.=50/Aм.
tв./tм.=(50/Aв.)/(50/Aм)=Aв./Aм.=3

Answer 2

Problem Analysis

We are given that a motorcyclist and a cyclist start from rest and undergo uniformly accelerated motion. 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 time it takes for the motorcyclist.

Solution

Let's assume the acceleration of the cyclist is a m/s² and the acceleration of the motorcyclist is 3a m/s². We need to find the ratio of the time it takes for the cyclist to reach a speed of 50 km/h to the time it takes for the motorcyclist.

To solve this problem, we can use the equations of motion for uniformly accelerated motion:

1. v = u + at (Equation 1) 2. v² = u² + 2as (Equation 2)

where: - v is the final velocity - u is the initial velocity (which is 0 in this case) - a is the acceleration - t is the time taken - s is the distance traveled

For the cyclist: - Initial velocity (u) = 0 m/s - Final velocity (v) = 50 km/h = 50 * (1000/3600) m/s = 500/36 m/s - Acceleration (a) = a m/s²

Using Equation 1, we can solve for t:

v = u + at 500/36 = 0 + a * t t = (500/36) / a (Equation 3)

For the motorcyclist: - Initial velocity (u) = 0 m/s - Final velocity (v) = 50 km/h = 50 * (1000/3600) m/s = 500/36 m/s - Acceleration (a) = 3a m/s²

Using Equation 1, we can solve for t:

v = u + at 500/36 = 0 + 3a * t t = (500/36) / (3a) (Equation 4)

To find the ratio of the time taken by the cyclist to the time taken by the motorcyclist, we can divide Equation 3 by Equation 4:

(t_cyclist / t_motorcyclist) = [(500/36) / a] / [(500/36) / (3a)] = (500/36) / (500/36) * (3a / a) = 3

Therefore, the time taken by the cyclist to reach a speed of 50 km/h is 3 times greater than the time taken by the motorcyclist.

Answer

The time taken by the cyclist to reach a speed of 50 km/h is 3 times greater than the time taken by the motorcyclist.