Q: A vector has components $$A_x = -3$$ and $$A_y = 4. $$What is the direction of the vector relative to the positive x-axis?

$$\\arctan(4/3)$$ above the negative x-axis

Question 1

A car travels in a straight line and its position as a function of time is given by $$x(t) = 4t^2$ + 2t + 1$$, where $$x is in $$meters and $$t is in $$seconds. What is the car's instantaneous velocity at $$t = 3 s$$?

Accepted Answer

$$v = 26 m/s$$

Question 2

A ball is thrown straight up with an initial velocity of $$20 m/s. $$Ignoring air resistance, how long does it take for the ball to return to the thrower's hand? (Take $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$4.08 s$$

Question 3

A car moving at $$15 m/s $$comes to a stop in $$1.5 s $$with constant acceleration. What is the magnitude of the car's acceleration?

Accepted Answer

$$a = 10 m/s$^2$$

Question 4

Which of the following statements about vectors is correct?

Accepted Answer

A vector has both magnitude and direction.

Question 5

A projectile is launched with an initial velocity of $$v_0 = 10$ m/s at an angle of 30^	$$ext{o}$$ above the horizontal. What is the initial vertical component of the velocity?

Accepted Answer

$$v_{0y} = 5 m/s$$

Question 6

A hiker walks $$3 km $$east and then $$4 km $$north. What is the magnitude of the hiker's displacement?

Accepted Answer

$$5 km$$

Question 7

A velocity-versus-time graph for an object moving with constant acceleration is:

Accepted Answer

A straight line with nonzero slope

Question 8

A rock is dropped from rest from a cliff and falls $$100 m $$before hitting the ground. What is its velocity just before impact? (Take $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$v = 44.3 m/s$$

Question 9

Which of the following best describes the acceleration of a ball at the very top of its trajectory when thrown straight up?

Accepted Answer

Negative

Question 10

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 11

A drag racer starts from rest and travels $$6.0 m in$$ $$1.0 s $$with constant acceleration. If the racer continues with the same acceleration, how far will it travel in $$5.0 s $$total?

Accepted Answer

$$150 m$$

Question 12

Which of the following is true about free fall (ignoring air resistance)?

Accepted Answer

All objects fall with the same acceleration regardless of mass.

Question 13

A car accelerates from rest at $$2 m/s$^2$$ for $$5 s. $$What is its final velocity?

Accepted Answer

$$10 m/s$$

Question 14

A vector $$\vec{B}$$ has a magnitude of $$10$$ and points $$60^	ext{o}$$ above the x-axis. What is the y-component of $$\vec{B}$$?

Accepted Answer

$$B_y = 8.66$$

Question 15

A cyclist rides at a constant velocity of $$7.0 m/s. $$How far does the cyclist travel in $$3.0$$ minutes?

Accepted Answer

$$1,260 m$$

Question 16

If a vector is multiplied by $$-1$$, what happens to the vector?

Accepted Answer

Its direction reverses, magnitude unchanged.

Question 17

A ball is thrown horizontally from a cliff with a speed of $$10 m/s. $$What is the initial vertical velocity?

Accepted Answer

$$0 m/s$$

Question 18

Which of the following is NOT a vector quantity?

Accepted Answer

Distance

Question 19

A car travels $$100 m $$north, then $$100 m $$east. What is the magnitude of its displacement?

Accepted Answer

$$141 m$$

Question 20

A vector has components $$A_x = -3$$ and $$A_y = 4. $$What is the direction of the vector relative to the positive x-axis?

Accepted Answer

$$\arctan(4/3)$$ above the negative x-axis

Physics with Calculus: Motion in One and Two Dimensions & Vectors

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