Q: A ball is thrown downward from a tower with an initial velocity of $$3.00\ \mathrm{m/s}. $$What is its position after $$2.00\ \mathrm{s}$$? (Assume $$g = 9.80\ \mathrm{m/s}^2$$ and initial position $$x_0 = 0$.)

$$x = 0 + 3.00 \times 2.00 + \frac{1}{2} \times 9.80 \times (2.00)^2$ = 3.00 \times 2.00 + 19.6 = 6.00 + 19.6 = 25.6\ \mathrm{m}$$

Q: A car accelerates from rest at $$2.00\ \mathrm{m/s}^2$$ across a $$30.0\ \mathrm{m}$$ intersection. How long does it take to cross?

$$t = \sqrt{\frac{2x}{a}} = \sqrt{\frac{2 \times 30.0}{2.00}} = \sqrt{30.0} \approx 5.48\ \mathrm{s}$$

Q: A ball is thrown upward with an initial velocity of $$15.0\ \mathrm{m/s}. $$How long is it in the air before returning to the thrower's hand? (Ignore air resistance, $$g = 9.80\ \mathrm{m/s}^2)$$

$$t = \frac{2 v_0$}{g} = \frac{2 \times 15.0}{9.80} \approx 3.06\ \mathrm{s}$$

Question 1

A car travels 100 m east, then 50 m west along a straight road. What is the car's displacement and total distance traveled?

Accepted Answer

Displacement: $$+50\ \mathrm{m}$$, Distance: $$150\ \mathrm{m}$$

Question 2

Which of the following statements best describes the difference between distance and displacement?

Accepted Answer

Distance is a scalar and measures the total path length; displacement is a vector and measures the straight-line change in position.

Question 3

A runner moves from $$x_1 = 50.0$$\ \mathrm{m}$$ to x_2$ = 30.5\ \mathrm{m} in$$ $$3.00\ \mathrm{s}. $$What is the runner's average velocity?

Accepted Answer

$$-6.5\ \mathrm{m/s}$$

Question 4

The position of a particle is given by $$x(t) = 5t^2$ + 3t - 1$$, where $$x is in $$meters and $$t in $$seconds. What is the instantaneous velocity at $$t = 2\ \mathrm{s}$$?

Accepted Answer

$$v = \frac{dx}{dt} = 10t + 3 = 23\ \mathrm{m/s}$$

Question 5

Which of the following is true about instantaneous velocity?

Accepted Answer

It is the slope of the tangent to the position vs. time curve at a given point.

Question 6

A car's velocity changes from $$-15.0\ \mathrm{m/s} to$$ $$-5.0\ \mathrm{m/s} in$$ $$2.0\ \mathrm{s}. $$What is the average acceleration?

Accepted Answer

$$a = \frac{-5.0 - (-15.0)}{2.0} = 5.0\ \mathrm{m/s}^2$$

Question 7

Which of the following scenarios describes deceleration?

Accepted Answer

A car moving east slows down while its acceleration points west.

Question 8

A ball is thrown downward from a tower with an initial velocity of $$3.00\ \mathrm{m/s}. $$What is its position after $$2.00\ \mathrm{s}$$? (Assume $$g = 9.80\ \mathrm{m/s}^2$$ and initial position $$x_0 = 0$.)

Accepted Answer

$$x = 0 + 3.00 	imes 2.00 + \frac{1}{2} 	imes 9.80 	imes (2.00)^2$ = 3.00 	imes 2.00 + 19.6 = 6.00 + 19.6 = 25.6\ \mathrm{m}$$

Question 9

A car accelerates from rest at $$2.00\ \mathrm{m/s}^2$$ across a $$30.0\ \mathrm{m}$$ intersection. How long does it take to cross?

Accepted Answer

$$t = \sqrt{\frac{2x}{a}} = \sqrt{\frac{2 	imes 30.0}{2.00}} = \sqrt{30.0} \approx 5.48\ \mathrm{s}$$

Question 10

Which of the following is NOT a valid equation for motion with constant acceleration?

Accepted Answer

$$x = x_0$ + v t^2$

Question 11

A ball is thrown upward with an initial velocity of $$15.0\ \mathrm{m/s}. $$How long is it in the air before returning to the thrower's hand? (Ignore air resistance, $$g = 9.80\ \mathrm{m/s}^2)$$

Accepted Answer

$$t = \frac{2 v_0$}{g} = \frac{2 	imes 15.0}{9.80} \approx 3.06\ \mathrm{s}$$

Question 12

Which of the following best describes the effect of air resistance on freely falling objects?

Accepted Answer

Air resistance causes objects of different shapes and masses to fall at different rates.

Question 13

A jet engine moves along a track with position $$x(t) = 2.10 t + 2.80$$, where $$x is in $$meters and $$t in $$seconds. What is the instantaneous velocity at $$t = 5.00\ \mathrm{s}$$?

Accepted Answer

$$v = \frac{dx}{dt} = 2.10\ \mathrm{m/s}$$

Question 14

Which of the following is the correct definition of average acceleration?

Accepted Answer

$$a_{avg} = \frac{v_2$ - v_1$}{t_2$ - t_1$}$$

Question 15

A ball is dropped from rest from a tall building. How far does it fall in the first $$3.00\ \mathrm{s}$$? (Assume $$g = 9.80\ \mathrm{m/s}^2)$$

Accepted Answer

$$x = \frac{1}{2} g t^2$ = \frac{1}{2} 	imes 9.80 	imes (3.00)^2$ = 44.1\ \mathrm{m}$$

Question 16

Which of the following steps is NOT part of the recommended problem-solving strategy for kinematics?

Accepted Answer

Guess the answer based on intuition.

Question 17

A car moves with constant velocity. Which of the following statements is true?

Accepted Answer

Its acceleration is zero.

Question 18

A person walks 20 m east, then 30 m west. What is the magnitude of the displacement?

Accepted Answer

$$|\Delta x| = |20 - 30| = 10\ \mathrm{m}$$

Kinematics in One Dimension: Structured Study Notes

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