Q: The figure represents the velocity of a particle as it travels along the x-axis. At what value(s) of $$t is $$the instantaneous acceleration equal to zero?

$$t = 0.5 s$\ \text{and}\ t = 2 s$$

Q: You are riding a Ferris wheel with radius $$R$$ that rotates at a constant speed. When you are at an angle $$\theta$$ below the horizontal and a distance $$h$$ above the ground, you release a small ball that travels a horizontal distance $$L$$ from your location. What must the period $$T of $$the Ferris wheel be?

$$T = \frac{2\pi R \cos\theta}{L} \sqrt{\frac{2h}{g}}$$

Question 1

A stone is thrown at an angle above the horizontal and feels negligible air resistance. Which of the graphs below best depicts the stone’s speed $$v as a $$function of time while in the air?

Accepted Answer

Graph (b)

Question 2

Under what condition is $$|\vec{A} - \vec{B}| = A + B$$?

Accepted Answer

Vectors $$\vec{A}$$ and $$\vec{B}$$ point in opposite directions.

Question 3

The figure represents the velocity of a particle as it travels along the x-axis. At what value(s) of $$t is $$the instantaneous acceleration equal to zero?

Accepted Answer

$$t = 0.5 s$\ 	ext{and}\ t = 2 s$$

Question 4

Two objects are dropped from a bridge, an interval of $$1.0 s $$apart, and experience no appreciable air resistance. As time progresses, the difference in their speeds:

Accepted Answer

remains constant.

Question 5

Which of the following motions is described by a motion diagram showing equally spaced dots in a straight line?

Accepted Answer

An ice skater gliding across the ice

Question 6

A particle revolves in a horizontal circle of radius $$R. At a $$particular instant, the magnitude of its acceleration is $$a$$, and its direction makes an angle $$	heta to $$its direction of motion. What is the speed $$v at $$this moment?

Accepted Answer

$$v = \sqrt{aR}$$

Question 7

A lion accelerates at $$a_\ell to a $$top speed $$v_\ell$$, and a gazelle accelerates at $$a_g to a $$top speed $$v_g$$ ($$v_g \u003e v_\ell). At $$the moment their speeds match, how much further has the lion traveled than the gazelle?

Accepted Answer

$$\frac{v_\$$ell^2$$}{2a_\ell} - \frac{v_\$$ell^2$$}{2a_g}$$

Question 8

A small plane flies at $$v_p in $$still air. If the wind blows directly west to east at $$v_w$$ and the plane is intended to end a distance $$d$$ directly north of its current location, how long will it take to travel that distance?

Accepted Answer

$$t = \frac{d}{\sqrt{v_p^2$ - v_w^2$}}$$

Question 9

You are riding a Ferris wheel with radius $$R$$ that rotates at a constant speed. When you are at an angle $$	heta$$ below the horizontal and a distance $$h$$ above the ground, you release a small ball that travels a horizontal distance $$L$$ from your location. What must the period $$T of $$the Ferris wheel be?

Accepted Answer

$$T = \frac{2\pi R \cos	heta}{L} \sqrt{\frac{2h}{g}}$$

Question 10

A salmon swims upstream against a current flowing south at speed $$v$$ and steers away from an obstacle by swimming at speed $$v\sqrt{2} in a $$direction $$45^\circ$$ north of east. What is the velocity of the salmon with respect to the ground?

Accepted Answer

$$v \hat{i}$$

Question 11

Which of the following statements is false?

Accepted Answer

If you are given an object's speed, you can definitely determine its velocity.

Question 12

Given any two vectors, which statement is correct?

Accepted Answer

The sum of the two vectors cannot be perpendicular to both vectors.

Question 13

You toss a ball into the air at an initial angle $$45^\circ$$ from the horizontal. At what point in the ball’s trajectory does the ball have the smallest speed? Neglect air resistance.

Accepted Answer

at the highest point in its flight

Question 14

The acceleration vector of a particle in uniform circular motion:

Accepted Answer

points toward the center of the circle.

Question 15

A motorized flying toy is attached to the lower end of a string of length $$L$$, and the other end is attached to the ceiling. The string makes a constant angle $$	heta$$ with the vertical as the ball moves at constant speed in a horizontal circle. If it takes the toy $$T$$ seconds to complete one revolution, what is the magnitude of the radial acceleration?

Accepted Answer

$$a = \frac{4\pi^2$ L \sin	heta}{T^2$}$$

Question 16

A small object begins a free-fall from rest from a height $$H$$ above the ground. At the same time a second small object is launched vertically upward from the ground with initial velocity $$v_0. At $$what height above the ground will the two objects first meet?

Accepted Answer

$$y = \frac{H + \frac{v_0$^2}{2g}}{1}$$

Question 17

A rocket follows a trajectory given by $$\vec{r}(t) = bt^2$ \hat{i} + ct^3$ \hat{j}$$, where $$b$$ and $$c$$ are positive constants. At what time will the acceleration vector point exactly $$45^\circ$$ between the $$x$$ and $$y$$ axes?

Accepted Answer

$$t = \sqrt{\frac{2b}{6c}}$$

Question 18

A helicopter flying at height $$h at $$constant horizontal speed $$v_h is to $$release a package so that it lands in a car traveling at constant speed $$v_c. At $$what angle $$	heta to $$the horizontal should the car be in the helicopter’s sights when the package is released?

Accepted Answer

$$	heta = \arctan\left(\frac{2h g}{v_h^2$}ight)$$

Physics 10310 Exam #1 – Step-by-Step Guidance for Selected Questions

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드