Q: A ball is thrown downward with an initial velocity of $$5\ \mathrm{m/s}$$ from a height of $$20\ \mathrm{m}. $$What is its velocity just before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s}^2)$$

$$v = \sqrt{5^2$ + 2 \times 9.8 \times 20} = \sqrt{5^2$ + 392} = \sqrt{417} \approx 20.4\ \mathrm{m/s}$$ downward

Question 1

Which of the following best describes the difference between displacement and distance for a particle moving along a straight line?

Accepted Answer

Displacement is the change in position and can be positive or negative, while distance is the total path length and always positive.

Question 2

A runner completes a lap around a 400 m track, ending at her starting point after 100 seconds. What is her average velocity?

Accepted Answer

$$v_{avg} = 0\ \mathrm{m/s}$$

Question 3

Which representation is NOT typically used to describe the motion of a car in kinematics?

Accepted Answer

Auditory representation

Question 4

A car moves from position $$x_i = -20\ \mathrm{m} to$$ $$x_f = 30\ \mathrm{m} in 10 $$seconds. What is its average velocity?

Accepted Answer

$$v_{avg} = \frac{30\ \mathrm{m} - (-20\ \mathrm{m})}{10\ \mathrm{s}} = 5\ \mathrm{m/s}$$

Question 5

Which statement about instantaneous velocity is correct?

Accepted Answer

It is the slope of the tangent to the position-time graph at a given instant.

Question 6

A ball is thrown straight upward with an initial velocity of $$v_0 = 15$$\ \mathrm{m/s}$$. What is its velocity at the maximum height?

Accepted Answer

$$v = 0\ \mathrm{m/s}$$

Question 7

Which kinematic equation can be used to find the final velocity of a particle under constant acceleration, given its initial velocity, acceleration, and displacement?

Accepted Answer

$$v_f^2$ = v_0$^2 + 2 a (x - x_0$)$$

Question 8

A car travels 100 m east, then 60 m west in 40 seconds. What is its displacement and average velocity?

Accepted Answer

Displacement: $$40\ \mathrm{m}$$ east, $$v_{avg} = 1\ \mathrm{m/s}$$ east

Question 9

If a particle moves with constant acceleration $$a$$, which of the following is true about its velocity-time graph?

Accepted Answer

The graph is a straight line with slope $$a.$$

Question 10

A stone is dropped from rest from a cliff. Neglecting air resistance, what is its velocity after 3 seconds?

Accepted Answer

$$v = 29.4\ \mathrm{m/s}$$ downward

Question 11

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration can be positive, negative, or zero.

Question 12

A car starts from rest and accelerates uniformly at $$2\ \mathrm{m/s}^2$$ for 5 seconds. What is its final velocity?

Accepted Answer

$$v = 10\ \mathrm{m/s}$$

Question 13

Which of the following is a vector quantity?

Accepted Answer

Displacement

Question 14

A ball is thrown downward with an initial velocity of $$5\ \mathrm{m/s}$$ from a height of $$20\ \mathrm{m}. $$What is its velocity just before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s}^2)$$

Accepted Answer

$$v = \sqrt{5^2$ + 2 	imes 9.8 	imes 20} = \sqrt{5^2$ + 392} = \sqrt{417} \approx 20.4\ \mathrm{m/s}$$ downward

Question 15

Which of the following is the correct calculus-based expression for displacement in terms of velocity?

Accepted Answer

$$x_f = x_i + \int_{t_i}^{t_f} v\,dt$$

Question 16

A car moves with constant velocity $$v = 12\ \mathrm{m/s}$$ for 8 seconds. How far does it travel?

Accepted Answer

$$x = 96\ \mathrm{m}$$

Question 17

Which of the following is NOT a step in the general problem-solving strategy described in the study materials?

Accepted Answer

Memorize

Question 18

A ball is thrown upward with velocity $$v_0 = 20$$\ \mathrm{m/s}$$. How long does it take to reach its maximum height? (Use g = 9.8$$\ \mathrm{m/s}^2$$)

Accepted Answer

$$t = \frac{20}{9.8} \approx 2.04\ \mathrm{s}$$

Question 19

Which of the following statements about the acceleration of a freely falling object near Earth's surface is correct?

Accepted Answer

Its magnitude is $$g = 9.80\ \mathrm{m/s}^2$$ downward.

(CH2) Kinematics in One Dimension: Study Notes

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