Question

двигаясь равноускоренно автомобиль за 2с прошел 60м и увеличил скорость в трое. Найдите начальную и конечную скорости автомобиля на этом пути.

Answer 1

a=(v-vo)/t=2vo/2=vo

S=vot+at^2/2

60=2vo+2vo

60=4v0

vo=15 м/с

3vo=45м/с

Answer 2

Problem Analysis

We are given that a car moves with constant acceleration and covers a distance of 60 meters in 2 seconds. Additionally, the car increases its speed threefold during this time. We need to find the initial and final velocities of the car during this motion.

Solution

Let's assume the initial velocity of the car is v0 and the final velocity is v. We are also given that the car covers a distance of 60 meters in 2 seconds.

Using the equation of motion for uniformly accelerated linear motion:

s = v0t + (1/2)at^2

where: - s is the distance covered (60 meters), - v0 is the initial velocity, - t is the time taken (2 seconds), and - a is the acceleration.

Since the car moves with constant acceleration, we can use the equation:

v = v0 + at

where: - v is the final velocity.

We are also given that the car increases its speed threefold during this time. This means the final velocity is three times the initial velocity:

v = 3v0

Now, let's solve for the initial and final velocities.

Calculation

Substituting the given values into the equation of motion, we have:

60 = v0(2) + (1/2)a(2)^2

Simplifying, we get:

60 = 2v0 + 2a

Rearranging the equation, we have:

a = (60 - 2v0) / 2

Substituting the value of v = 3v0 into the equation v = v0 + at, we have:

3v0 = v0 + a(2)

Substituting the value of a from the previous equation, we get:

3v0 = v0 + [(60 - 2v0) / 2] * 2

Simplifying, we have:

3v0 = v0 + 60 - 2v0

Simplifying further, we get:

2v0 = 60

Dividing both sides by 2, we find:

v0 = 30

Substituting the value of v0 = 30 into the equation v = 3v0, we have:

v = 3(30) = 90

Therefore, the initial velocity of the car is 30 m/s and the final velocity is 90 m/s.

Answer

The initial velocity of the car is 30 m/s and the final velocity is 90 m/s.