Question

ゆめら

（1）がわかりません。
答えは4.0sの時なのですが、AとＢの速度が一緒になった時になぜ距離が最大になるのか分かりません。

思考
27.2 物体の運動 物体AとBが,図のv-tグラフ
のような速度で, 一直線上を動いている。 時刻 t=0s
のとき,両者は同じ位置にあったとして,次の各問に
答えよ。
(1) 0≦t≦8.0s の範囲において, AとBの間の距離
が最大となる時刻は何か。
↑v[m/s]
8.0
2.0
0
A
4.0
B
(2) 0≦t≦8.0s の範囲において, AとBの間の距離
が最大のとき, その値は何mか。
(3) AがBに追いつく時刻 tは何sか。
(4) 0≦t≦8.0s の範囲において,時刻 0s での位置からの移動距離 x[m〕を縦軸,時刻
t[s]を横軸にとり, A, B の x-tグラフを1つの図にまとめて描け。
(岐阜聖徳学園大改)
t[s]
8.0

Answer 1

✨ ベストアンサー ✨

Dw

Let's imagine that if you want to catch up with someone today, and they are 100 steps away from you. Assume they start at (100,0), and you start at (0,0). Let's say both of you have the same stride length, but they can take four steps per second while you can only take two steps per second.

At t=0 seconds, the distance between you two is 100 steps.

At t=1 second, they are at (104,0) and you are at (2,0), making the distance 102 steps.

To catch up, you increase your speed to three steps per second.

At t=2 seconds, they are at (108,0), and you are at (5,0), creating a distance of 103 steps.

Realizing you're not catching up, you decide to match their speed and run at four steps per second.

From t=3 seconds onwards, they will be at (108+4n), and you will be at (5+4n), with a constant distance of 103 steps.

Dw

Alternatively, if there's someone running at the same maximum speed as you, starting slightly ahead, you'll forever trail behind. Despite having the same speed, the initial head start ensures a constant distance between you two.

Dw

Because as long as your speeds are the same, the distance between you two will no longer increase.

ゆめら

The analogy is too easy to understand! I understood it very well! ! I'm not good at physics, so this is really helpful. thank you!