Question

Две материальные точки движутся по оси Os по законам:s=2t+4 и s=4t Встретятся ли эти точки? Если да, то в какой момент времени? Нарисуйте графики движения и с их помощью поясните полученные результаты.как??? как это сделать? подскажите, прошу

Answer 1

в обоих случаях графики---прямые линии
"Встретятся ли эти точки"===пересекутся ли эти прямые ??? ДА
"В какой момент времени"===при каком значении t (или х)... т.е. надо найти t при кот. s равны
s = 2t + 4 = 4t
4t - 2t = 4
2t = 4
t = 2 (s=8) на графике это будет точка пересечения прямых...

 

Answer 2

Solving the Problem of Two Moving Points

To solve the problem of two material points moving along the Os axis according to the laws s=2t+4 and s=4t, we can follow these steps:

1. Determine if the Points Will Meet: - We need to find out if and when these two points will meet. 2. Find the Meeting Time: - If the points will meet, we need to determine the moment in time when they will do so.

3. Graphical Representation: - We can use the given laws of motion to plot the graphs of the points' movements and analyze the results.

Let's proceed with these steps.

Determining if the Points Will Meet

The positions of the two points are given by the laws s=2t+4 and s=4t. To find out if the points will meet, we need to solve the equation s=2t+4 for t and then substitute this value into the equation s=4t. If the resulting s values are the same, the points will meet.

Finding the Meeting Time

Let's solve the equation s=2t+4 for t: ``` s = 2t + 4 2t = s - 4 t = (s - 4)/2 ``` Now, substitute this value of t into the equation s=4t: ``` s = 4t s = 4((s - 4)/2) s = 2s - 8 s = -8 (This is not possible as time cannot be negative) ``` Since the resulting s value is negative, it means the points will not meet.

Graphical Representation

The graphical representation of the points' movements can help us visualize the situation. We can plot the graphs of s=2t+4 and s=4t to understand their movements.

The graph of s=2t+4 is a straight line with a slope of 2 and a y-intercept of 4. The graph of s=4t is also a straight line with a slope of 4 and passing through the origin.

By analyzing these graphs, we can see that the two lines will not intersect, confirming our earlier conclusion that the points will not meet.

In summary, the two material points described by the laws s=2t+4 and s=4t will not meet as their paths do not intersect.