Q: A car's position is given by $$x(t) = bt - ct^2$, where b = 8.40$$\ \mathrm{m/s}$$ and c = 0.610$$\ \mathrm{$$m/s^2$$}$$. What is the instantaneous velocity at t = 5.40$$\ \mathrm{s}$$?

$$8.40 - 2 \times 0.610 \times 5.40 = 1.80\ \mathrm{m/s}$$

Question 1

Given two vectors $$\vec{A}$$ and $$\vec{B}$$ with components $$\vec{A} = 3\hat{i} + 4\hat{j}$$ and $$\vec{B} = -4\hat{i} + 3\hat{j}$$, what is the magnitude of their sum $$\vec{C} = \vec{A} + \vec{B}$$?

Accepted Answer

$$5\sqrt{2}$$

Question 2

If two vectors of equal magnitude are perpendicular to each other, which of the following is equal to zero?

Accepted Answer

Their scalar (dot) product

Question 3

On a velocity versus time graph for one-dimensional motion, what does the slope of the tangent line at any point represent?

Accepted Answer

Instantaneous acceleration

Question 4

A ball is thrown straight up and reaches its maximum height. Ignoring air resistance, at what point(s) is the acceleration NOT equal to $$9.80\ \mathrm{m/s^2$}$$ downward?

Accepted Answer

None of these

Question 5

If the acceleration of an object in one-dimensional motion is a linear function of time, what is the highest exponent of time in the equation for its position?

Accepted Answer

Three

Question 6

For any motion, the vector for average acceleration over a time interval always points in the same direction as the vector for which quantity measured over that interval?

Accepted Answer

Change in velocity

Question 7

For projectile motion with negligible air resistance, which property of the object's motion remains constant throughout the flight?

Accepted Answer

The horizontal component of the velocity

Question 8

An object moves in a circle and slows down at a steady rate. What is the direction of its acceleration vector?

Accepted Answer

It has both a component toward the center and a component opposite the direction of motion

Question 9

A car's position is given by $$x(t) = bt - ct^2$, where b = 8.40$$\ \mathrm{m/s}$$ and c = 0.610$$\ \mathrm{$$m/s^2$$}$$. What is the instantaneous velocity at t = 5.40$$\ \mathrm{s}$$?

Accepted Answer

$$8.40 - 2 	imes 0.610 	imes 5.40 = 1.80\ \mathrm{m/s}$$

Question 10

A volcano on Earth ejects rocks vertically to a maximum height of $$150\ \mathrm{m}. If a $$volcano on Mars ejects rocks with the same initial velocity, how high will they go on Mars? (Mars gravity $$g_{Mars} = 3.71\ \mathrm{m/s^2$}$$, Earth gravity $$g_{Earth} = 9.80\ \mathrm{m/s^2$})$$

Accepted Answer

$$396\ \mathrm{m}$$

Question 11

A fireman uses a hose to shoot water at $$27.0\ \mathrm{m/s} at an $$angle $$	heta$$ above the horizontal. The water takes $$3.40\ \mathrm{s} to $$reach a building $$48.0\ \mathrm{m}$$ away. What is the value of $$	heta$$?

Accepted Answer

$$10.2^\circ$$

Question 12

A Ferris wheel with radius $$19.0\ \mathrm{m}$$ completes one revolution every $$16.0\ \mathrm{s}. $$What is the magnitude of the acceleration of a passenger at the rim?

Accepted Answer

$$1.46\ \mathrm{m/s^2$}$$

Question 13

Which kinematic equation for constant acceleration would you use to solve for the time when an object is at a given height twice during its flight?

Accepted Answer

$$y = y_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 14

At what point(s) along a projectile’s trajectory (ignoring air resistance) is the velocity vector perpendicular to the acceleration vector?

Accepted Answer

At the highest point

Question 15

An object traveling in a circle slows down to one third of its original speed. By what factor does its centripetal acceleration change?

Accepted Answer

It decreases by a factor of $$9$$

Question 16

Given vectors $$\vec{A} = 7.20\hat{i} - 3.50\hat{j}$$ and $$\vec{B} = -4.10\hat{i} + 6.90\hat{j}$$, what is the angle between them?

Accepted Answer

$$133^\circ$$

Question 17

A projectile is launched from ground level with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Which of the following best describes the horizontal acceleration during flight (ignoring air resistance)?

Accepted Answer

$$0$$

Question 18

A car moves such that its position is $$x(t) = 8.40t - 0.610t^2$. What is the average velocity between t = 3.70$$\ \mathrm{s}$$ and t = 9.20$$\ \mathrm{s}$$?

Accepted Answer

$$-0.98\ \mathrm{m/s}$$

Question 19

A Ferris wheel passenger passes through the lowest point of the circle. What is the direction of her acceleration at that instant?

Accepted Answer

Directly upward

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