Q: A vector $$ extbf{A}$$ has a magnitude of $$10$$ units and points at an angle of $$30^ ext{o}$$ above the x-axis. What is its $$ extbf{i}$$ and $$ extbf{j}$$ component form?

$$\textbf{A} = 10\cos30^ ext{o}\textbf{i} + 10\sin30^ ext{o}\textbf{j}$$

Q: If a vector $$\textbf{B}$$ has components $$\textbf{B} = 3\textbf{i} - 4\textbf{j}$$, what is its magnitude?

$$|\textbf{B}| = \sqrt{3^2$ + (-4)^2$} = 5$$

Q: A stone is thrown upward with an initial velocity of $$12 m/s. $$What is its velocity after $$1.5 s$$? (Assume $$g = 9.8 m/s$^2$$ downward)

$$v = 12 - 9.8 \times 1.5 = -2.7 m/s$

Question 1

A car moves along a straight road such that its position as a function of time is given by $$x(t) = 3t^2$ + 2t + 1 ($$where $$x is in $$meters and $$t in $$seconds). What is the instantaneous acceleration of the car at $$t = 2 s$$?

Accepted Answer

$$a = 6 m/s$^2$$

Question 2

Which of the following statements about projectile motion is correct?

Accepted Answer

The vertical component of velocity is zero at the projectile's maximum height.

Question 3

A vector $$	extbf{A}$$ has a magnitude of $$10$$ units and points at an angle of $$30^	ext{o}$$ above the x-axis. What is its $$	extbf{i}$$ and $$	extbf{j}$$ component form?

Accepted Answer

$$	extbf{A} = 10\cos30^	ext{o}	extbf{i} + 10\sin30^	ext{o}	extbf{j}$$

Question 4

A ball is thrown horizontally from the top of a $$20 m $$high building with an initial speed of $$5 m/s. $$How long does it take to hit the ground? (Assume $$g = 9.8 m/s$^2)$$

Accepted Answer

$$t = \sqrt{\dfrac{20}{9.8}} \approx 1.43 s$$

Question 5

Which of the following best describes uniform motion?

Accepted Answer

Velocity is constant and acceleration is zero.

Question 6

A cyclist accelerates from rest with a constant acceleration of $$2 m/s$^2. $$What is her velocity after $$4$$ seconds?

Accepted Answer

$$v = 8 m/s$$

Question 7

The area under a velocity vs. time graph represents:

Accepted Answer

Displacement

Question 8

A car is moving east with velocity $$v = 20 m/s $$and accelerates west with $$a = -5 m/s$^2. $$What happens to the car's speed?

Accepted Answer

The car slows down.

Question 9

If the position of an object is given by $$x(t) = 4t^3$ - 2t^2$ + t$$, what is the velocity at $$t = 1 s$$?

Accepted Answer

$$v = 10 m/s$$

Question 10

A projectile is launched with an initial speed $$v_i = 15 m/s at an $$angle $$	heta = 45^	ext{o}$$ above the horizontal. What is the initial vertical component of velocity?

Accepted Answer

$$v_{iy} = 15\sin45^	ext{o}$$

Question 11

A particle moves in a circle of radius $$r = 2 m $$with a constant speed $$v = 4 m/s. $$What is its centripetal acceleration?

Accepted Answer

$$a_c = \dfrac{v^2$}{r} = \dfrac{16}{2} = 8 m/s$^2$$

Question 12

Which of the following is true about the direction of acceleration?

Accepted Answer

Acceleration is always in the direction of the change in velocity ($$\Delta v).$$

Question 13

A runner starts at $$x = 0$$ and runs with a constant velocity of $$6 m/s $$for $$10$$ seconds. What is her displacement?

Accepted Answer

$$\Delta x = 60 m$$

Question 14

If a vector $$	extbf{B}$$ has components $$	extbf{B} = 3	extbf{i} - 4	extbf{j}$$, what is its magnitude?

Accepted Answer

$$|	extbf{B}| = \sqrt{3^2$ + (-4)^2$} = 5$$

Question 15

A projectile is launched from ground level with an initial velocity $$v_i = 20 m/s at$$ $$30^	ext{o}$$ above the horizontal. What is the horizontal component of velocity?

Accepted Answer

$$v_{ix} = 20\cos30^	ext{o}$$

Question 16

A car's velocity changes from $$10 m/s to$$ $$2 m/s in$$ $$4$$ seconds. What is its average acceleration?

Accepted Answer

$$a_{av} = \dfrac{2 - 10}{4} = -2 m/s$^2$$

Question 17

A stone is thrown upward with an initial velocity of $$12 m/s. $$What is its velocity after $$1.5 s$$? (Assume $$g = 9.8 m/s$^2$$ downward)

Accepted Answer

$$v = 12 - 9.8 	imes 1.5 = -2.7 m/s$

Question 18

Which of the following is NOT a characteristic of non-uniform motion?

Accepted Answer

Velocity is constant.

Question 19

A car travels along a curved path at constant speed. Which statement is true?

Accepted Answer

The car has a nonzero acceleration directed toward the center of the curve.

Question 20

If the velocity of an object is given by $$v(t) = 5t^2$, what is its acceleration at t = 3$ s?

Accepted Answer

$$a = \dfrac{d}{dt}(5t^2$) = 10t$$,\ a = 30$$ m/s^2$

Study Guide: Motion and Kinematics (Chapters 1–4, Physics with Calculus)

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