Question

Велосипедист двигался равномерно по прямой дороге со скоростью 15 м/с.когда лн поравнялся с неподвижным автомобилем ,тот начал двигаться с ускорением 2м/с..через какое время автомобиль догонит велосепидиста? какова будет скорость автомобилиста в этот момент?

Answer 1

Путь, который проедет велосипедист, равен s=vt=15t. Автомобиль проедет тот же путь за время догона велосипеда, но с ускорением s=att/2. Получим vt=att/2. t=2v/a=30/2=15 c. Скорость автомобиля в этот момент V=Vo+at=at=2·15=30 м/с. Начальная скорость автомобиля Vo=0 по условию .

Answer 2

Problem Analysis

We are given that a cyclist is moving uniformly with a speed of 15 m/s on a straight road. When the cyclist reaches a stationary car, the car starts moving with an acceleration of 2 m/s². We need to determine the time it takes for the car to catch up to the cyclist and the speed of the car at that moment.

Solution

To solve this problem, we can use the equations of motion. Let's denote the time it takes for the car to catch up to the cyclist as t.

The equation of motion for the cyclist is: s_cyclist = v_cyclist * t (Equation 1)

The equation of motion for the car is: s_car = u_car * t + (1/2) * a_car * t² (Equation 2)

In Equation 1, s_cyclist represents the distance traveled by the cyclist, v_cyclist represents the speed of the cyclist, and t represents time.

In Equation 2, s_car represents the distance traveled by the car, u_car represents the initial velocity of the car (which is 0 since it starts from rest), a_car represents the acceleration of the car, and t represents time.

Since the car catches up to the cyclist, the distance traveled by both the car and the cyclist will be the same. Therefore, we can equate Equations 1 and 2:

v_cyclist * t = (1/2) * a_car * t² (Equation 3)

Simplifying Equation 3, we get:

t = (2 * v_cyclist) / a_car (Equation 4)

Now, we can substitute the given values into Equation 4 to calculate the time it takes for the car to catch up to the cyclist.

To find the speed of the car at that moment, we can substitute the calculated value of t into Equation 2 and solve for u_car (initial velocity of the car).

Let's perform the calculations.

Calculation

Given: - Speed of the cyclist (v_cyclist) = 15 m/s - Acceleration of the car (a_car) = 2 m/s²

Using Equation 4, we can calculate the time (t) it takes for the car to catch up to the cyclist:

t = (2 * v_cyclist) / a_car

Substituting the given values:

t = (2 * 15) / 2 = 15 seconds

Therefore, it takes 15 seconds for the car to catch up to the cyclist.

To find the speed of the car at that moment, we can substitute the calculated value of t into Equation 2 and solve for u_car (initial velocity of the car):

s_car = u_car * t + (1/2) * a_car * t²

Since the car starts from rest, the initial velocity (u_car) is 0. Therefore, the equation simplifies to:

s_car = (1/2) * a_car * t²

Substituting the values:

s_car = (1/2) * 2 * 15² = 225 meters

Therefore, the speed of the car at the moment it catches up to the cyclist is 0 m/s (since it starts from rest) and the distance traveled by the car is 225 meters.

Answer

The car will catch up to the cyclist after 15 seconds and the speed of the car at that moment will be 0 m/s. The car will have traveled a distance of 225 meters.

Please let me know if anything is unclear or if you need further assistance!