Quiz 1 英文版 (请在8分钟内完成5道题目)

The kinetic energy动能of a particle, E, varies directly as the square of its speed, v. The kinetic energy of the particle is 200 joules if it is moving at a speed of [latex] 5ms^{-1}[/latex]. Find the speed of the particle if it has a kinetic energy of 650 joules.

[latex] ?ms^{-1}[/latex]

note: joule 焦耳 [能量的计算单位]

The area of a sector of a circle, A varies directly as the angle of the sector, , and the square of the radius 半径, r. The area of the sector with radius 6cm and the angle at the centre of [latex]\frac{11}{6}[/latex] radian is [latex]33cm^{2} [/latex]. Find the area of a sector of a circle with the radius of 7cm and the angle at the centre of 1.8radian.

[latex]?cm^{2} [/latex]

note: radian 弧度 [角度的另一个计算单位，[latex]1rad \approx 57.29[/latex] ]

Eight men can build a bridge in 14days. Find the time, taken in days, for five men to build the similar bridge. [Assume that all the men have the same skills and can work at the same rate].

At a sports camp, there is sufficient food for 81 athletes to last 8 days. If 27 athletes are absent for the camp, how long can the food last? [Assume that each athlete is given the same amount of food for each meal]

When an object is pulled by a constant 持续 force , the acceleration 加速度 of the object varies inversely with its mass. An object with a mass of 4 kg will move with an acceleration of [latex]1.5ms^{-2}[/latex]. Find the acceleration of the object if its mass is 10kg.

[latex]?ms^{-2}[/latex]

note: [latex]Acceleration= \frac{velocity速度}{time时间}[/latex]