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一支队伍沿平直的公路匀速前进，其速度的大小为v1，队伍全长为L．一个通讯兵从队尾以速度v2(v2>v1)赶到队前然后立即原速返回队尾，求这个过程中通信兵通过的路...

Mar 19, 2024

一支队伍沿平直的公路匀速前进，其速度的大小为v1，队伍全长为L．一个通讯兵从队尾以速度v2(v2>v1)赶到队前然后立即原速返回队尾，求这个过程中通信兵通过的路程和位移

Solution

Calculate the time it takes for the communication soldier to reach the front of the team

Use the equation

t = \frac{L}{v_2 - v_1}

to find the time. Since the soldier is moving at a speed of

v_2

and the team is moving at

v_1

, the relative speed is

v_2 - v_1

Calculate the distance the soldier travels to reach the front

Use the equation

d_{\text{to front}} = v_2 t

to find the distance

Calculate the time it takes for the soldier to return to the back of the team

Use the equation

t = \frac{L}{v_2 + v_1}

for the return trip, since the relative speed is now

v_2 + v_1

Calculate the distance the soldier travels to return to the back

Use the equation

d_{\text{to back}} = v_2 t

to find the distance

Add the distances to find the total distance traveled

Use the equation

D_{\text{total}} = d_{\text{to front}} + d_{\text{to back}}

to find the total distance

Calculate the displacement of the soldier

Since the soldier returns to the starting point, the displacement is

\Delta x = 0

Answer

The total distance traveled by the communication soldier is

2Lv_2/(v_2^2 - v_1^2)

and the displacement is 0.

Key Concept

In kinematics, the total distance traveled is the sum of all individual distances covered, regardless of direction, while displacement is the change in position from the initial to the final point, which is a vector quantity.

Explanation

The communication soldier travels a certain distance to the front of the team and the same distance back, resulting in a total distance that is the sum of these two distances. However, since the soldier ends up at the starting point, the displacement is zero.