Q: A car accelerates uniformly from rest and covers a distance of 100 m in 5 seconds. What is the magnitude of its acceleration?

$$a = \frac{2 \times 100}{5^2$} = 8\ \text{m/s}^2$$

Q: A ball is thrown upward with an initial velocity of $$v_0 = 20$$\ \text{m/s}$$. Ignoring air resistance, what is the maximum height reached by the ball?

$$h = \frac{v_0$^2}{2g} = \frac{20^2$}{2 \times 9.8} = 20.4\ \text{m}$$

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

$$|\textbf{A}| = \sqrt{A_x^2$ + A_y^2$} = \sqrt{3^2$ + 4^2$} = 5$$

Q: A projectile is launched at an angle $$\theta = 30^\circ$$ with an initial speed $$v_0 = 40$$\ \text{m/s}$$. What is the horizontal range of the projectile? (Assume g = 9.8$$\ \text{m/s}^2$$)

$$R = \frac{v_0$^2 \sin 2\theta}{g} = \frac{40^2$ \sin 60^\circ}{9.8} \approx 141\ \text{m}$$

Q: A stone is dropped from a height of 45 m. How long does it take to reach the ground? (Assume $$g = 9.8\ \text{m/s}^2)$$

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

Q: If a vector $$\textbf{B} is $$rotated by $$90^\circ in $$the plane, which of the following statements is true?

The magnitude of $$\textbf{B}$$ remains unchanged.

Q: A train moves with constant acceleration. Its velocity increases from $$10\ \text{m/s} to$$ $$30\ \text{m/s} in 5 $$seconds. What is the acceleration?

$$a = \frac{\Delta v}{\Delta t} = \frac{30 - 10}{5} = 4\ \text{m/s}^2$$

Q: A projectile is launched from ground level with an initial velocity $$v_0 at an $$angle $$\theta. $$Which equation gives the time of flight?

$$T = \frac{2 v_0$ \sin \theta}{g}$$

Q: A vector $$\textbf{C}$$ has a magnitude of 10 and points at an angle of $$60^\circ$$ from the x-axis. What is its y-component?

$$C_y = 10 \sin 60^\circ = 10 \times 0.866 = 8.66$$

Question 1

A car accelerates uniformly from rest and covers a distance of 100 m in 5 seconds. What is the magnitude of its acceleration?

Accepted Answer

$$a = \frac{2 	imes 100}{5^2$} = 8\ 	ext{m/s}^2$$

Question 2

Which of the following best describes the trajectory of a projectile launched horizontally from the top of a cliff?

Accepted Answer

A parabolic curve

Question 3

A ball is thrown upward with an initial velocity of $$v_0 = 20$$\ 	ext{m/s}$$. Ignoring air resistance, what is the maximum height reached by the ball?

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{20^2$}{2 	imes 9.8} = 20.4\ 	ext{m}$$

Question 4

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

Accepted Answer

$$|	extbf{A}| = \sqrt{A_x^2$ + A_y^2$} = \sqrt{3^2$ + 4^2$} = 5$$

Question 5

A projectile is launched at an angle $$	heta = 30^\circ$$ with an initial speed $$v_0 = 40$$\ 	ext{m/s}$$. What is the horizontal range of the projectile? (Assume g = 9.8$$\ 	ext{m/s}^2$$)

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g} = \frac{40^2$ \sin 60^\circ}{9.8} \approx 141\ 	ext{m}$$

Question 6

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration is the rate of change of velocity with respect to time.

Question 7

A stone is dropped from a height of 45 m. How long does it take to reach the ground? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

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

Question 8

If a vector $$	extbf{B} is $$rotated by $$90^\circ in $$the plane, which of the following statements is true?

Accepted Answer

The magnitude of $$	extbf{B}$$ remains unchanged.

Question 9

A train moves with constant acceleration. Its velocity increases from $$10\ 	ext{m/s} to$$ $$30\ 	ext{m/s} in 5 $$seconds. What is the acceleration?

Accepted Answer

$$a = \frac{\Delta v}{\Delta t} = \frac{30 - 10}{5} = 4\ 	ext{m/s}^2$$

Question 10

A projectile is launched from ground level with an initial velocity $$v_0 at an $$angle $$	heta. $$Which equation gives the time of flight?

Accepted Answer

$$T = \frac{2 v_0$ \sin 	heta}{g}$$

Question 11

A vector $$	extbf{C}$$ has a magnitude of 10 and points at an angle of $$60^\circ$$ from the x-axis. What is its y-component?

Accepted Answer

$$C_y = 10 \sin 60^\circ = 10 	imes 0.866 = 8.66$$

Question 12

A car travels east for 40 km, then north for 30 km. What is the magnitude of its displacement?

Accepted Answer

$$d = \sqrt{40^2$ + 30^2$} = \sqrt{1600 + 900} = \sqrt{2500} = 50\ 	ext{km}$$

Question 13

Which of the following is NOT a scalar quantity?

Accepted Answer

Velocity

Question 14

A projectile is launched at $$45^\circ$$ with a speed of $$20\ 	ext{m/s}. $$What is the maximum height reached? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$h = \frac{(v_0$ \sin \$$theta)^2$$}{2g} = \frac{(20 	imes 0.707)^2$}{2 	imes 9.8} \approx 5.1\ 	ext{m}$$

Question 15

A cyclist increases her speed from $$5\ 	ext{m/s} to$$ $$15\ 	ext{m/s} in 4 $$seconds. What is her average acceleration?

Accepted Answer

$$a = \frac{15 - 5}{4} = 2.5\ 	ext{m/s}^2$$

Question 16

A ball is thrown horizontally from a height of 20 m with a speed of $$10\ 	ext{m/s}. $$How far from the base of the building does it land? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} \approx 2.02\ 	ext{s}$$; $$d = v_x t = 10 	imes 2.02 = 20.2\ 	ext{m}$$

Question 17

Which mathematical operation is used to find the component of a vector along a given axis?

Accepted Answer

Dot product

Question 18

A car moves with a velocity given by $$v(t) = 3t^2$. What is the displacement between t = 0$ and t = 2$ seconds?

Accepted Answer

$$s = \$$int_0$$^2 3t^2$ dt = [t^3$]_0^2$ = 8 - 0 = 8\ 	ext{m}$$

Question 19

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$Which of the following best describes the vertical velocity at the peak of its trajectory?

Accepted Answer

The vertical velocity is zero.

Physics with Calculus: Essential Mathematics, Linear Motion, and Projectile Motion

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