CalcGospel 國際數學圖譜
返回

M2 2022 Oct Q2

A Level / Edexcel / M2

IAL 2022 Oct Paper · Question 2

题目

Problem

2.

A car of mass 900 kg900\,\mathrm{kg} is moving down a straight road which is inclined at an angle α\alpha to the horizontal, where sin⁡α=112\sin\alpha=\frac1{12}

The engine of the car is working at a constant rate of 15 kW15\,\mathrm{kW}. The resistance to the motion of the car is modelled as a constant force of magnitude 400 N400\,\mathrm{N}.

Find the acceleration of the car at the instant when it is moving at 16 m s−116\,\mathrm{m\,s^{-1}}

(5)
题目中文翻译

质量为 900 kg900\,\mathrm{kg} 的汽车沿一条与水平面成 α\alpha 角的直路下坡，其中 sin⁡α=112\sin\alpha=\frac1{12}。

汽车发动机以恒定功率 15 kW15\,\mathrm{kW} 工作。 将汽车所受的运动阻力视为大小为 400 N400\,\mathrm{N} 的恒力。

求汽车以 16 m s−116\,\mathrm{m\,s^{-1}} 的速率行驶的瞬间的加速度。

(5)

解答

解法一

思路

展开

发动机功率先从千瓦换成瓦，再除以瞬时速率求牵引力。汽车下坡，重力沿坡分量与牵引力同向，阻力反向。

答题过程

展开

The driving force at 16 m s−1^{-1} is

F=1500016=937.5 N.F=\frac{15000}{16}=937.5\text{ N}.

Taking down the road as positive and applying Newton’s second law,

F+900gsin⁡α−400=900a.F+900g\sin\alpha-400=900a.

With sin⁡α=1/12\sin\alpha=1/12,

937.5+900(9.8)(112)−400=900a.937.5+900(9.8)\left(\frac1{12}\right)-400=900a.

Therefore

a=1.41 m s−2 down the road.\boxed{a=1.41\text{ m s}^{-2}\text{ down the road}}.