Q: Which of the following statements about the vector (cross) product is correct?

The vector product is anti-commutative: $$\vec{A} \times \vec{B} = -\vec{B} \times \vec{A}.$$

Question 1

Which of the following statements about the vector (cross) product is correct?

Accepted Answer

The vector product is anti-commutative: $$\vec{A} 	imes \vec{B} = -\vec{B} 	imes \vec{A}.$$

Question 2

Given the position-time graph of a particle, what does the slope of the line connecting two points on the curve represent?

Accepted Answer

The average velocity between the two points.

Question 3

A ball is thrown vertically upward with an initial velocity of $$15.0\ \mathrm{m/s}. $$What is the maximum height it reaches above the starting point? (Assume $$g = 9.80\ \mathrm{m/s^2$})$$

Accepted Answer

$$y_1$$ = \dfrac{(15.0\ \mathrm{m/s}$$)^2$$}{2(9.80\ \mathrm{$$m/s^2$$})} = 11.5\ \mathrm{m}$$

Question 4

At the highest point in the motion of a ball thrown straight upward, which of the following is true?

Accepted Answer

Its velocity is zero and its acceleration is negative (downward).

Question 5

Which kinematic equation would you use to find the final velocity $$v of an $$object after traveling a displacement $$\Delta x$$ with constant acceleration $$a$$ and initial velocity $$v_0$$?

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a$$\Delta x$$

Question 6

A car moves along the x-axis such that its position as a function of time is $$x(t) = 2t^2$ + 3t + 1. $$What is the instantaneous velocity at $$t = 2\ \mathrm{s}$$?

Accepted Answer

$$v = \dfrac{dx}{dt} = 4t + 3;\ v(2) = 11\ \mathrm{m/s}$$

Question 7

If a velocity-time graph is a straight line with a negative slope, what does this indicate about the object's motion?

Accepted Answer

The object is accelerating in the negative direction.

Question 8

A ball is thrown upward from a building with an initial velocity of $$15.0\ \mathrm{m/s}. $$What is its velocity when it is $$5.00\ \mathrm{m}$$ above the release point? (Take $$g = 9.80\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_y = \pm 11.3\ \mathrm{m/s}$$

Question 9

Which of the following best describes the relationship between average velocity and instantaneous velocity?

Accepted Answer

Average velocity is the slope of the secant line between two points on the position-time graph, while instantaneous velocity is the slope of the tangent at a single point.

Question 10

A particle moves along a straight line with constant acceleration. If its initial velocity is $$v_0$$ and its acceleration is $$a$$, what is its position after time $$t$$?

Accepted Answer

$$x = x_0$ + v_0$ t + \dfrac{1}{2} a t^2$

Question 11

On a position-time graph, what does the concavity (curvature) of the graph at a point indicate?

Accepted Answer

The object's acceleration at that point.

Question 12

A student drops a ball from rest from the top of a building. Ignoring air resistance, which equation gives the ball's position $$y$$ after time $$t$$?

Accepted Answer

$$y = y_0$ + v_0$ t + \dfrac{1}{2} (-g) t^2$

Question 13

A car accelerates from rest at $$2.0\ \mathrm{m/s^2$}$$ for $$5.0\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = v_0$ + at = 0 + (2.0\ \mathrm{m/s^2$})(5.0\ \mathrm{s}) = 10\ \mathrm{m/s}$$

Question 14

Which of the following is true about the acceleration of an object in free fall near Earth's surface (ignoring air resistance)?

Accepted Answer

It is constant and directed downward.

Question 15

A runner moves along a straight path such that her velocity changes from $$2.0\ \mathrm{m/s} to$$ $$6.0\ \mathrm{m/s} in$$ $$4.0\ \mathrm{s}. $$What is her average acceleration?

Accepted Answer

$$a_{av} = \dfrac{6.0 - 2.0}{4.0} = 1.0\ \mathrm{m/s^2$}$$

Question 16

If the velocity-time graph of a particle is a horizontal line above the time axis, what can you conclude about the particle's motion?

Accepted Answer

The particle is moving with constant positive velocity.

Question 17

A ball is thrown vertically upward from the edge of a cliff with an initial velocity $$v_0. $$Which equation would you use to find the time when the ball returns to the same height from which it was thrown?

Accepted Answer

$$y = y_0$ + v_0$ t + \dfrac{1}{2} (-g) t^2$

Kinematics: Motion Along a Straight Line and Vector Products

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드