Question

Поезд, идущий со скоростью 15 м/с, остановился через 20 с после начала торможения. считая, что торможение происходило с постоянным ускорением, определите перемещение поезда за 20 с

Answer 1

tх=20с

V0x=15 м/с

a-0.5 м.с2

Решение:

Sx=V0t+ axt2:2=  -v0/t=vot-vot2^2t=vot/2=15x20:2=150м

 

Answer 2

Calculation of the Train's Displacement

To determine the displacement of the train during the 20 seconds of braking, we can use the equation of motion for uniformly accelerated motion:

\[s = ut + \frac{1}{2}at^2\]

Where: - s is the displacement (unknown) - u is the initial velocity of the train (15 m/s) - t is the time taken for braking (20 s) - a is the acceleration during braking (unknown)

To find the acceleration, we can use the equation:

\[v = u + at\]

Where: - v is the final velocity of the train (0 m/s)

Rearranging the equation, we have:

\[a = \frac{v - u}{t}\]

Substituting the given values, we can calculate the acceleration:

\[a = \frac{0 - 15}{20}\]

Simplifying, we find:

\[a = -0.75 \, \text{m/s}^2\]

Now, we can substitute the values of u, t, and a into the equation for displacement:

\[s = ut + \frac{1}{2}at^2\]

\[s = 15 \times 20 + \frac{1}{2} \times (-0.75) \times (20)^2\]

Simplifying, we find:

\[s = 300 - 150\]

Therefore, the displacement of the train during the 20 seconds of braking is 150 meters.