Two bodies began to move in one direction from one point with an interval of 10 s: one uniformly at a speed of 5 m / s, and the other uniformly accelerated without an initial speed with an acceleration of 2 m / s ^ 2. How many seconds will the second body reach the first?
We will count the time from the moment the first body begins to move. After some time t, the second body will catch up with the first. Time of movement of the second body: t – 10 s. Both bodies at the moment t have passed the same path:
S = V₀t;
S = a (t-10) ² / 2;
V₀t = a (t-10) ² / 2.
Substitute the values from the condition:
5t = 2 (t² – 20t + 100) / 2;
5t = t² – 20t + 100;
t² – 25t + 100 = 0.
t₁ = (25 + √ (625-400)) / 2 = 20 s.
t₂ = (25 – √ (625-400)) / 2 = 5 s.
We discard the second root (the second body has not even begun to move in 5 seconds).
Answer: The second body will catch up with the first body in 20 seconds.
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