Kinematics运动学

Which pair lists one scalar and one vector, in that order?下列哪组依次列出了一个标量和一个矢量？

• (A) velocity, speed速度，速率
• (B) distance, displacement路程，位移
• (C) displacement, distance位移，路程
• (D) acceleration, force加速度，力

A particle's position is $x(t) = 3t^2 - 12t + 5$ (SI units). Its velocity at $t=2~\mathrm{s}$ is质点的位置为 $x(t) = 3t^2 - 12t + 5$（SI 单位）。其在 $t=2~\mathrm{s}$ 时的速度为

• (A) $-12~\mathrm{m/s}$
• (B) $0~\mathrm{m/s}$
• (C) $6~\mathrm{m/s}$
• (D) $12~\mathrm{m/s}$

For the same particle as Q2, its acceleration is对于 Q2 中的同一质点，其加速度为

• (A) zero everywhere处处为零
• (B) $6~\mathrm{m/s^2}$ constant（恒定）
• (C) $-12~\mathrm{m/s^2}$ constant（恒定）
• (D) $6t~\mathrm{m/s^2}$

The velocity vs. time graph below describes a particle moving along the $x$-axis.下图为一质点沿 $x$ 轴运动的速度-时间图像。

During which interval is the particle's acceleration negative and nonzero?在哪段时间区间内，质点的加速度为负且不为零？

• (A) $0 < t < 2~\mathrm{s}$
• (B) $2 < t < 4~\mathrm{s}$
• (C) $4 < t < 6~\mathrm{s}$
• (D) nowhere on the graph图中任何地方均不满足

A car starts from rest and accelerates uniformly to $20~\mathrm{m/s}$ over $5~\mathrm{s}$. The distance it travels in this interval is一辆汽车从静止出发，在 $5~\mathrm{s}$ 内匀加速至 $20~\mathrm{m/s}$。该过程中行驶的路程为

• (A) $25~\mathrm{m}$
• (B) $50~\mathrm{m}$
• (C) $75~\mathrm{m}$
• (D) $100~\mathrm{m}$

A ball is dropped from rest from a height $H$ above level ground. Air resistance is negligible. Its speed just before impact is一只球从距水平地面高度 $H$ 处由静止释放，空气阻力不计。其落地前瞬间的速率为

• (A) $\sqrt{gH}$
• (B) $\sqrt{2gH}$
• (C) $2gH$
• (D) $gH$

A particle has acceleration $a(t) = 6t~\mathrm{m/s^2}$ and starts from rest at $x=0$. Its position at $t=2~\mathrm{s}$ is一质点的加速度为 $a(t) = 6t~\mathrm{m/s^2}$，从 $x=0$ 处由静止开始运动。其在 $t=2~\mathrm{s}$ 时的位置为

• (A) $4~\mathrm{m}$
• (B) $8~\mathrm{m}$
• (C) $12~\mathrm{m}$
• (D) $24~\mathrm{m}$

A boat heads due north across a river at $4~\mathrm{m/s}$ relative to the water. The river flows due east at $3~\mathrm{m/s}$. The boat's speed relative to the bank is一艘船相对于水以 $4~\mathrm{m/s}$ 的速度正北方向横渡河流，河流以 $3~\mathrm{m/s}$ 向正东方流动。船相对于河岸的速率为

• (A) $1~\mathrm{m/s}$
• (B) $5~\mathrm{m/s}$
• (C) $7~\mathrm{m/s}$
• (D) $\sqrt{7}~\mathrm{m/s}$

A ball is launched from ground level with initial speed $25~\mathrm{m/s}$ at $40^\circ$ above the horizontal. Take $g=9.8~\mathrm{m/s^2}$. Its time of flight (return to launch height) is closest to一只球以 $25~\mathrm{m/s}$ 的初速度从地面以仰角 $40^\circ$ 抛出，取 $g=9.8~\mathrm{m/s^2}$。其飞行时间（回到发射高度所需时间）最接近

• (A) $1.6~\mathrm{s}$
• (B) $2.6~\mathrm{s}$
• (C) $3.3~\mathrm{s}$
• (D) $5.1~\mathrm{s}$

A projectile is launched from ground level with speed $v_0$ at angle $\theta$. Neglect air resistance. Its horizontal range is maximized when $\theta$ equals一抛体以速度 $v_0$、仰角 $\theta$ 从地面发射，不计空气阻力。当 $\theta$ 等于多少时水平射程最大？

• (A) $30^\circ$
• (B) $45^\circ$
• (C) $60^\circ$
• (D) $90^\circ$

A particle's position is $x(t)=t^3 - 6t^2 + 9t$ (SI). On the interval $0 \le t \le 4~\mathrm{s}$, the particle's average velocity equals its instantaneous velocity at $t=$质点的位置为 $x(t)=t^3 - 6t^2 + 9t$（SI 单位）。在区间 $0 \le t \le 4~\mathrm{s}$ 上，质点的平均速度等于其瞬时速度时，$t=$

• (A) $1~\mathrm{s}$ only（仅此）
• (B) $2~\mathrm{s}$ only（仅此）
• (C) $2 \pm \dfrac{2\sqrt{3}}{3}~\mathrm{s}$
• (D) $2 \pm \dfrac{\sqrt{3}}{3}~\mathrm{s}$

A stone is thrown straight up from the edge of a $40~\mathrm{m}$ cliff with initial speed $15~\mathrm{m/s}$. Take $g=9.8~\mathrm{m/s^2}$ and ignore air resistance. The stone's speed when it strikes the ground at the cliff's base is closest to一块石头以 $15~\mathrm{m/s}$ 的初速度从 $40~\mathrm{m}$ 高的悬崖边缘竖直向上抛出，取 $g=9.8~\mathrm{m/s^2}$，忽略空气阻力。石头落到崖底时的速率最接近

• (A) $19~\mathrm{m/s}$
• (B) $23~\mathrm{m/s}$
• (C) $32~\mathrm{m/s}$
• (D) $43~\mathrm{m/s}$

A particle moves in the $xy$-plane with $\vec r(t) = (3t)\,\hat\imath + (4t - t^2)\,\hat\jmath$ (SI). Its speed at $t=1~\mathrm{s}$ is一质点在 $xy$ 平面内运动，其位置矢量为 $\vec r(t) = (3t)\,\hat\imath + (4t - t^2)\,\hat\jmath$（SI 单位）。其在 $t=1~\mathrm{s}$ 时的速率为

• (A) $2~\mathrm{m/s}$
• (B) $\sqrt{13}~\mathrm{m/s}$
• (C) $5~\mathrm{m/s}$
• (D) $\sqrt{18}~\mathrm{m/s}$

A particle's $a$ vs. $t$ graph is a triangle: $a$ rises linearly from $0$ at $t=0$ to $a_0$ at $t=T/2$, then falls linearly back to $0$ at $t=T$. If the particle starts from rest, its speed at $t=T$ is一质点的 $a$-$t$ 图像为三角形：加速度从 $t=0$ 时的 $0$ 线性增大至 $t=T/2$ 时的 $a_0$，再线性减小至 $t=T$ 时的 $0$。若质点从静止出发，其在 $t=T$ 时的速率为

• (A) $\dfrac{a_0 T}{4}$
• (B) $\dfrac{a_0 T}{2}$
• (C) $a_0 T$
• (D) $\dfrac{a_0 T^2}{2}$

A train moves due east at $20~\mathrm{m/s}$ relative to the ground. A passenger walks toward the front of the train at $1.5~\mathrm{m/s}$ relative to the train. The passenger's velocity relative to the ground is一列火车相对于地面以 $20~\mathrm{m/s}$ 向正东方行驶。一位乘客相对于火车以 $1.5~\mathrm{m/s}$ 向车头方向行走。该乘客相对于地面的速度为

• (A) $18.5~\mathrm{m/s}$ east向东
• (B) $20~\mathrm{m/s}$ east向东
• (C) $21.5~\mathrm{m/s}$ east向东
• (D) $\sqrt{20^2 + 1.5^2}~\mathrm{m/s}$ northeast东偏北

A particle moves along the $x$-axis with velocity $v(t) > 0$ that is decreasing in time. Which statement best describes the motion?一质点沿 $x$ 轴运动，其速度 $v(t) > 0$ 且随时间减小。下列哪个说法最能描述该运动？

• (A) The particle is moving in the $+x$ direction and speeding up.质点沿 $+x$ 方向运动且速率增大。
• (B) The particle is moving in the $+x$ direction and slowing down.质点沿 $+x$ 方向运动且速率减小。
• (C) The particle is moving in the $-x$ direction and speeding up.质点沿 $-x$ 方向运动且速率增大。
• (D) The particle is at rest.质点静止。

From the same height above level ground, ball A is dropped from rest at the same instant ball B is launched horizontally. Air resistance is negligible. Which ball lands first?球 A 从同一高度由静止释放，同时球 B 从同一高度水平抛出，空气阻力不计。哪个球先落地？

• (A) Ball A (dropped)球 A（自由落体）
• (B) Ball B (horizontal)球 B（水平抛出）
• (C) They land simultaneously.两球同时落地。
• (D) Depends on ball B's horizontal speed.取决于球 B 的水平速度。

A projectile is launched horizontally from a cliff of height $h$ with initial speed $v_0$. Air resistance is negligible. Its speed at the moment of impact is一抛体以初速度 $v_0$ 从高度为 $h$ 的悬崖顶端水平抛出，空气阻力不计。其落地瞬间的速率为

• (A) $v_0$
• (B) $\sqrt{v_0^2 + gh}$
• (C) $\sqrt{v_0^2 + 2gh}$
• (D) $v_0 + \sqrt{2gh}$