The only means to create a real image with a single lens would be to place $(a)$ the object inside the focal length of a converging lens. $(b)$ the object inside the focal length of a diverging lens. $(c)$ the object outside the focal length of a converging lens. $(d)$ the object outside the focal length of a diverging lens. $(e)$ Any of the above, given the correct distance from the focal point.

Plot the expressios on each side of the equals symbol to find whether the equation is an identity. If the equation looks like an identity, then prove it algebraically.

$$\frac{1}{1+\sin x}+\frac{1}{1-\sin x}=\sec ^2 x$$

The diagram in Figure 2-30 tracks the location of an object moving in a straight line along the x axis. Assume that the object is at the origin at t = 0. Of the five times shown, which time (or times) represents when the object is

(d) moving away from the origin?

Underline the gerund in the following sentences. Then, identify the function of the gerund by writing above it one of these abbreviations :S for subject, PN for predicate nominative, $D O$ for direct object, 10 for indirect object, or $O P$ for object of a preposition.

My favorite pastime is definitely reading.

As an object in rectilinear motion moves, its signed distance s from the origin at time t is given by the position function $s=s(t)=\frac{1}{6} t^{4}-t^{2}+\frac{1}{2} t+4$, where s is in meters and t is in seconds. (a) Find the velocity v, acceleration a, jerk J, and snap S of the object at any time t. (b) Find the velocity of the object at t=0 and at t=3. (c) Find the acceleration of the object at t=0. Interpret your answer. (d) Is the jerk of the object constant? In your own words, explain what the jerk says about the acceleration of the object. (e) How would you interpret the snap for this object in rectilinear motion?

Use the following information. The diagram shows how similar triangles relate to human vision. An image similar to a viewed object appears on the retina. The actual height of the object h is proportional to the size of the image as it appears on the retina r. In the same manner, the distances from the object to the lens of the eye $d$ and from the lens to the retina, $25 \mathrm{~mm}$ in the diagram, are also proportional. An object that is 1 meter tall appears on the retina as $1 \mathrm{~mm}$ tall. How far away is the object?

The position function of an object moving horizontally along a straight line as a function of time is $s(t)-t^2-3 t+2, t \geq 0$, in metres, at time $t$, in seconds.

(a). Determine the velocity and acceleration of the object.

(b). Determine the position of the object when the velocity is 0 .

(c). Determine the speed of the object when the position is 0 .

(d). When does the object move to the left?

(e). Determine the average velocity from $t=2$ to $t=5$.

Underline the gerund in the following sentences. Then, identify the function of the gerund by writing above it one of these abbreviations :S for subject, PN for predicate nominative, $D O$ for direct object, 10 for indirect object, or $O P$ for object of a preposition.

The puppy's constant whimpering worried us.

The theory of relativity predicts that when an object moves at speeds close to the speed of light, the object appears heavier. The apparent, or relativistic, mass, $m$, of the object when it is moving at speed $v$ is given by the formula

$$m=\frac{m_0}{\sqrt{1-v^2 / c^2}},$$

where $c$ is the speed of light and $m_0$ is the mass of the object when it is at rest.

(a) Use the formula for $m$ to decide what values of $v$ are possible.

An object of mass $60$ kg starts from rest at the top of a $45^{\circ}$ inclined plane. Assume that the coefficient of kinetic friction is $0.05$ (see Problem $18$). If the force due to air resistance is proportional to the velocity of the object, say, $-3v$, find the equation of motion of the object. How long will it take the object to reach the bottom of the inclined plane if the incline is $10$m long?

a. Differentiate both sides of the identity cos $2 t=\cos ^{2} t-\sin ^{2} t$ to prove that sin 2t=2 sin t cos t. b. Verify that you obtain the same identity for sin 2t as in part (a) if you differentiate the identity cos $2 t=2 \cos ^{2} t-1$. c. Differentiate both sides of the identity sin 2t=2 sin t cos t to prove that $\cos 2 t=\cos ^{2} t-\sin ^{2} t$.

The only means to create a real image with a single lens would be to place $(a)$ the object inside the focal length of a converging lens; $(b)$ the object inside the focal length of a diverging lens; $(c)$ the object outside the focal length of a converging lens; $(d)$ the object outside the focal length of a diverging lens; $(e)$ any of the above, given the correct distance from the focal point.

"Two spherical objects differ in size and mass. Object $A$ has a mass that is eight times the mass of object $B$. The radius of object $A$ is twice the radius of the object $B$. How do their densities compare? $(a)$ $\rho_{\text{A}}>\rho_{\text{B}^{\prime}}$, $(b)$ $\rho_{\text{A}}<\rho_{\text{B}^{\prime}}$ $(c)$ $\rho_{\text{A}}=\rho_{\text{B}^{\prime}}$, $(d)$ Not enough information is given to compare their densities."

The coordinates of an object moving in the xy plane vary with time according to the equations x = -5.00 sin $\omega$t and y = 4.00 - 5.00 cos $\omega$t, where $\omega$ is a constant, x and y are in meters, and t is in seconds. (a) Determine the components of velocity of the object at t = 0. (b) Determine the components of acceleration of the object at t = 0. (c) Write expressions for the position vector, the velocity vector, and the acceleration vector of the object at any time t > 0. (d) Describe the path of the object in an xy plot.