Q: A ball is dropped from a height of 20 m. Ignoring air resistance, how long does it take to reach the ground? (Use $$g = 9.8 m/s$^2)$$

$$t = \sqrt{\frac{2 \times 20}{9.8}} \approx 2.02 s$$

Q: A student throws a rock horizontally from a cliff. If the cliff is 45 m high, how long does it take for the rock to hit the ground? (Ignore air resistance, $$g = 9.8 m/s$^2)$$

$$t = \sqrt{\frac{2 \times 45}{9.8}} \approx 3.03 s$$

Q: A ball is thrown straight up with an initial velocity of $$15 m/s. $$What is its velocity after $$2$$ seconds? (Take $$g = 9.8 m/s$^2)$$

$$v = 15 - 9.8 \times 2 = -4.6 m/s$$

Question 1

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

Accepted Answer

$$v = 14 m/s$$

Question 2

Which of the following statements about vectors is TRUE?

Accepted Answer

Vectors can be added graphically using the tail-to-tip method.

Question 3

A projectile is launched from the ground at an angle $$	heta$$ above the horizontal with initial speed $$v_0. $$What is the horizontal component of its initial velocity?

Accepted Answer

$$v_0$$ \cos 	heta$$

Question 4

A ball is dropped from a height of 20 m. Ignoring air resistance, how long does it take to reach the ground? (Use $$g = 9.8 m/s$^2)$$

Accepted Answer

$$t = \sqrt{\frac{2 	imes 20}{9.8}} \approx 2.02 s$$

Question 5

Which of the following is a scalar quantity?

Accepted Answer

Speed

Question 6

A student throws a rock horizontally from a cliff. If the cliff is 45 m high, how long does it take for the rock to hit the ground? (Ignore air resistance, $$g = 9.8 m/s$^2)$$

Accepted Answer

$$t = \sqrt{\frac{2 	imes 45}{9.8}} \approx 3.03 s$$

Question 7

A car accelerates from rest at a constant rate of $$2 m/s$^2. $$How far does it travel in $$5$$ seconds?

Accepted Answer

$$s = 25 m$\quad ($$using $$s = \frac{1}{2} a t^2$)

Question 8

Which equation correctly relates displacement, initial velocity, acceleration, and time for constant acceleration?

Accepted Answer

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

Question 9

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

Accepted Answer

$$5$$

Question 10

A train moves with constant velocity. Which of the following statements is TRUE?

Accepted Answer

The train's acceleration is zero.

Question 11

A projectile is launched at $$30^\circ$$ above the horizontal with speed $$20 m/s. $$What is the vertical component of its initial velocity?

Accepted Answer

$$20 \sin 30^\circ = 10 m/s$$

Question 12

Which of the following best describes the area under a velocity vs. time graph?

Accepted Answer

It represents the object's displacement.

Question 13

A ball is thrown straight up with an initial velocity of $$15 m/s. $$What is its velocity after $$2$$ seconds? (Take $$g = 9.8 m/s$^2)$$

Accepted Answer

$$v = 15 - 9.8 	imes 2 = -4.6 m/s$$

Question 14

A vector $$\vec{B} is $$subtracted from vector $$\vec{A}$$ ($$\vec{A} - \vec{B}). $$Which of the following is TRUE?

Accepted Answer

The result is a vector pointing from the tip of $$\vec{B} to $$the tip of $$\vec{A}.$$

Question 15

A skier slides down a frictionless ramp inclined at $$30^\circ to $$the horizontal. What is the acceleration of the skier along the ramp?

Accepted Answer

$$a = g \sin 30^\circ = 4.9 m/s$^2$$

Question 16

Which of the following is NOT a correct use of significant figures?

Accepted Answer

Reporting a measurement as 2.00 m when the instrument reads 2 m.

Question 17

A car moves with velocity $$v = 10 m/s $$east for $$5 s$$, then $$v = 10 m/s $$north for $$5 s. $$What is the magnitude of its displacement from the starting point?

Accepted Answer

$$70.7 m$\quad ($$using $$\sqrt{50^2$ + 50^2$})$$

Question 18

A projectile is launched horizontally from a height $$h$$ with initial speed $$v_0. $$Which equation gives the time to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Question 19

A vector $$\vec{C}$$ has magnitude $$10$$ and points at $$60^\circ$$ above the x-axis. What are its x and y components?

Accepted Answer

$$C_x = 10 \cos 60^\circ = 5$$, $$C_y = 10 \sin 60^\circ = 8.66$$

Exam 1 Study Guide: Motion in One and Two Dimensions (Chapters 1–3)

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