Question

поезд двигающийся со скоростью 54 км/ч и ускорение 0,25м/с2 увеличил скорость до 72 км/ч. Определить время за которое это произошло и путь​

Answer 1

Calculation of Time and Distance

To determine the time it took for the train to increase its speed and the distance covered during that time, we can use the equations of motion.

The initial speed of the train is 54 km/h, and it increases to 72 km/h with an acceleration of 0.25 m/s².

We can convert the speeds from km/h to m/s by multiplying them by 1000/3600.

The equations we can use are:

1. Final velocity = Initial velocity + (acceleration * time) 2. Distance = Initial velocity * time + (0.5 * acceleration * time²)

Let's calculate the time and distance.

Calculation:

Given: - Initial velocity (u) = 54 km/h - Final velocity (v) = 72 km/h - Acceleration (a) = 0.25 m/s²

Converting the velocities to m/s: - Initial velocity (u) = 54 * (1000/3600) m/s ≈ 15 m/s - Final velocity (v) = 72 * (1000/3600) m/s ≈ 20 m/s

Using the first equation, we can find the time (t): v = u + (a * t) 20 = 15 + (0.25 * t) 5 = 0.25t t = 5 / 0.25 t = 20 seconds

So, it took 20 seconds for the train to increase its speed.

Using the second equation, we can find the distance (s): s = u * t + (0.5 * a * t²) s = 15 * 20 + (0.5 * 0.25 * 20²) s = 300 + (0.5 * 0.25 * 400) s = 300 + 50 s = 350 meters

Therefore, the train covered a distance of 350 meters during the time it took to increase its speed.

Summary: - Time taken to increase speed: 20 seconds - Distance covered during that time: 350 meters

Please note that these calculations assume constant acceleration throughout the entire process.