Question

Локомотив через 15 с после начала движения развил скорость о,5 м/с. Через какое время после начала движения скорость локомотива станет 3 м/с? Какой путь пройдёт локомотив за это время ? Движение локомотива считать равноускоренным.

Answer 1

Напишем формулу для скорости равноускоренного движения
V1=Vo+a*t1
Vo-равно 0 - так как локомотив начал движение с нулевой скорости.
найдем ускорение зная, что через 15 сек V1 стала = 0,5м/с
0.5=0+a*15
a=0.5/15=1/30 м/с^2
Тогда найдем время через которое скорость стала 3 м/с
V2=a*t2
t2=V2/a=3/(1/30)=90 секунд
Для расстояния
S=Vo*t2+a*t2^2/2
S=a*t^2/2=(1/30)*90^2/2=135 м

Answer 2

Problem Analysis

We are given that a locomotive reaches a speed of 0.5 m/s after 15 seconds of starting its motion. We need to find out how much time it will take for the locomotive to reach a speed of 3 m/s and the distance it will cover during that time. The motion of the locomotive is assumed to be uniformly accelerated.

Solution

Let's use the equations of uniformly accelerated motion to solve this problem.

The equations of uniformly accelerated motion are:

1. v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. 2. s = ut + (1/2)at^2, where s is the distance covered, u is the initial velocity, a is the acceleration, and t is the time.

We are given that the initial velocity (u) is 0 m/s, the final velocity (v) is 3 m/s, and the acceleration (a) is constant.

Let's calculate the time it will take for the locomotive to reach a speed of 3 m/s using the first equation:

3 = 0 + a * t

Simplifying the equation, we get:

t = 3 / a

Now, let's calculate the distance covered by the locomotive during this time using the second equation:

s = 0 * t + (1/2) * a * t^2

Simplifying the equation, we get:

s = (1/2) * a * t^2

Substituting the value of t from the first equation, we get:

s = (1/2) * a * (3 / a)^2

Simplifying the equation, we get:

s = (1/2) * a * (9 / a^2)

Simplifying further, we get:

s = (9 / 2a)

Now, let's calculate the values of t and s.

Calculation

Given that the acceleration (a) is 0.5 m/s^2, we can calculate the time (t) it will take for the locomotive to reach a speed of 3 m/s:

t = 3 / 0.5 = 6 seconds

We can also calculate the distance (s) covered by the locomotive during this time:

s = (9 / 2 * 0.5) = 9 meters

Answer

Therefore, it will take the locomotive 6 seconds to reach a speed of 3 m/s, and it will cover a distance of 9 meters during this time.