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小汽车匀速行驶在公路上，坐在副驾驶位置的小红观察到小汽车速度表的指针始终在100km/h位置处，在超越相邻车道上同向匀速行驶的另一辆约10m长大客车的过程中，小...

Mar 19, 2024

小汽车匀速行驶在公路上，坐在副驾驶位置的小红观察到小汽车速度表的指针始终在100km/h位置处，在超越相邻车道上同向匀速行驶的另一辆约10m长大客车的过程中，小红发现自己通过大客车的时间为5s，则下列四个选项中最接近大客车速度的是（） A．30km/h B．60km/h C．78km/h D．93km/h

Solution

Convert the speed of the small car from km/h to m/s:

100 \text{ km/h} = \frac{100 \times 1000}{3600} \text{ m/s} = \frac{100}{3.6} \text{ m/s}

Calculate the distance the small car travels during the overtaking process:

d_{\text{car}} = v_{\text{car}} \times t = \frac{100}{3.6} \text{ m/s} \times 5 \text{ s}

Calculate the length of the distance covered by the small car relative to the bus:

d_{\text{relative}} = d_{\text{car}} - \text{length of the bus}

Calculate the relative speed of the small car with respect to the bus:

v_{\text{relative}} = \frac{d_{\text{relative}}}{t}

Calculate the speed of the bus in m/s and convert it to km/h:

v_{\text{bus}} = v_{\text{car}} - v_{\text{relative}}

Convert the speed of the bus to km/h:

v_{\text{bus}} \text{ (in km/h)} = v_{\text{bus}} \text{ (in m/s)} \times \frac{3600}{1000}

Answer

The speed of the bus is closest to 93 km/h.

Key Concept

In kinematics, the relative velocity between two objects is the vector difference between their velocities. It is used to calculate how fast one object is moving with respect to another.

Explanation

By calculating the relative velocity of the small car with respect to the bus and knowing the car's speed, we can determine the bus's speed.