Question

Автобус движется с постоянной скоростью 40 километров в час . С какой скоростью должен двигаться другое транспортное средство для того, чтобы скорость изменения расстояния между ними равнялась 60 км.ч.? Найди два варианта ответа на этот вопрос:1) при движении в одном и том же направлении, 2)при движение в противоположных направлениях. Проиллюстрируй каждый вариант найденного ответа на схемах движения из одной точки.

Answer 1

40+60=100 км/ч - скорость второго тр. ср. при движении в одном направлении

60-40=20 км/ч - скорость второго тр. ср. при движении в противоположных направлениях

Answer 2

Calculation of the Required Speed

To find the speed at which the other vehicle should move in order to maintain a constant rate of change of distance between the two vehicles, we can use the formula:

Required Speed = Speed of the First Vehicle ± Rate of Change of Distance

In this case, the speed of the first vehicle (the bus) is given as 40 km/h, and the rate of change of distance is given as 60 km/h. We need to find the required speed for two scenarios: when the vehicles are moving in the same direction and when they are moving in opposite directions.

1) Vehicles Moving in the Same Direction

When the vehicles are moving in the same direction, the required speed of the second vehicle can be calculated by subtracting the rate of change of distance from the speed of the first vehicle.

Required Speed = Speed of the First Vehicle - Rate of Change of Distance

Substituting the given values:

Required Speed = 40 km/h - 60 km/h = -20 km/h

Therefore, the second vehicle should move at a speed of -20 km/h (negative sign indicating that it is moving in the opposite direction) to maintain a rate of change of distance of 60 km/h.

2) Vehicles Moving in Opposite Directions

When the vehicles are moving in opposite directions, the required speed of the second vehicle can be calculated by adding the rate of change of distance to the speed of the first vehicle.

Required Speed = Speed of the First Vehicle + Rate of Change of Distance

Substituting the given values:

Required Speed = 40 km/h + 60 km/h = 100 km/h

Therefore, the second vehicle should move at a speed of 100 km/h to maintain a rate of change of distance of 60 km/h.

Illustration of the Two Scenarios

To illustrate the two scenarios, let's consider a point of reference and plot the motion of the two vehicles on a distance-time graph.

1) Vehicles Moving in the Same Direction:

In this scenario, the second vehicle is moving in the opposite direction to the first vehicle, but at a slower speed. As a result, the distance between the two vehicles decreases at a rate of 60 km/h.

Distance (km)
  |
  |     *
  |    *
  |   *
  |  *
  | *
  |*_______________________ Time (hours)
  0        1        2

2) Vehicles Moving in Opposite Directions:

In this scenario, the second vehicle is moving in the same direction as the first vehicle, but at a faster speed. As a result, the distance between the two vehicles increases at a rate of 60 km/h.

Distance (km)
  |
  |*
  | *
  |  *
  |   *
  |    *
  |     *
  |      *_________________ Time (hours)
  0        1        2

Please note that the above illustrations are for visualization purposes only and may not be to scale.

I hope this explanation helps! Let me know if you have any further questions.