Q: A car starts from rest and accelerates uniformly along a straight road. After 5 seconds, it reaches a speed of 20 m/s. What is the car's acceleration?

$$a = \frac{20\ \text{m/s}}{5\ \text{s}} = 4\ \text{m/s}^2$$

Q: A runner moves along a straight path. At $$t = 0 s$$, she is at $$x = 0 m. At$$ $$t = 10 s$$, she is at $$x = 50 m. $$What is her average velocity?

$$v_{\text{avg}} = \frac{50\ \text{m}}{10\ \text{s}} = 5\ \text{m/s}$$

Q: A ball is thrown vertically upward with an initial velocity of $$15\ \text{m/s}. $$Ignoring air resistance, what is the maximum height reached by the ball? (Use $$g = 9.8\ \text{m/s}^2)$$

$$h = \frac{v_0$^2}{2g} = \frac{(15)^2$}{2 \times 9.8} = 11.5\ \text{m}$$

Q: A train travels east for 100 km, then west for 40 km. What is the train's displacement?

$$\text{Displacement} = 100\ \text{km} - 40\ \text{km} = 60\ \text{km}$$\ east

Q: A particle moves along the x-axis according to $$x(t) = 3t^2$ + 2t + 1. $$What is the particle's velocity at $$t = 2 s$$?

$$v(t) = \frac{dx}{dt} = 6t + 2$$;\ at\ t = 2:\ v = 6 \times 2 + 2 = 14\ \text{m/s}$

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

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

Q: A cyclist travels at a constant speed of $$12\ \text{m/s}$$ for $$30\ \text{s}. $$How far does the cyclist travel?

$$d = v t = 12 \times 30 = 360\ \text{m}$$

Question 1

A car starts from rest and accelerates uniformly along a straight road. After 5 seconds, it reaches a speed of 20 m/s. What is the car's acceleration?

Accepted Answer

$$a = \frac{20\ 	ext{m/s}}{5\ 	ext{s}} = 4\ 	ext{m/s}^2$$

Question 2

Which of the following statements best describes displacement?

Accepted Answer

Displacement is a vector quantity that describes the change in position of an object.

Question 3

A runner moves along a straight path. At $$t = 0 s$$, she is at $$x = 0 m. At$$ $$t = 10 s$$, she is at $$x = 50 m. $$What is her average velocity?

Accepted Answer

$$v_{	ext{avg}} = \frac{50\ 	ext{m}}{10\ 	ext{s}} = 5\ 	ext{m/s}$$

Question 4

A ball is thrown vertically upward with an initial velocity of $$15\ 	ext{m/s}. $$Ignoring air resistance, what is the maximum height reached by the ball? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{(15)^2$}{2 	imes 9.8} = 11.5\ 	ext{m}$$

Question 5

Which of the following is NOT a scalar quantity?

Accepted Answer

Velocity

Question 6

A train travels east for 100 km, then west for 40 km. What is the train's displacement?

Accepted Answer

$$	ext{Displacement} = 100\ 	ext{km} - 40\ 	ext{km} = 60\ 	ext{km}$$\ east

Question 7

A particle moves along the x-axis according to $$x(t) = 3t^2$ + 2t + 1. $$What is the particle's velocity at $$t = 2 s$$?

Accepted Answer

$$v(t) = \frac{dx}{dt} = 6t + 2$$;\ at\ t = 2:\ v = 6 	imes 2 + 2 = 14\ 	ext{m/s}$

Question 8

Which equation best describes the position of an object undergoing constant acceleration?

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

A cyclist travels at a constant speed of $$12\ 	ext{m/s}$$ for $$30\ 	ext{s}. $$How far does the cyclist travel?

Accepted Answer

$$d = v t = 12 	imes 30 = 360\ 	ext{m}$$

Question 11

Which of the following best describes the difference between speed and velocity?

Accepted Answer

Speed is a scalar quantity; velocity is a vector quantity.

Question 12

A projectile is launched horizontally from a cliff with an initial speed of $$10\ 	ext{m/s}. If $$the cliff is $$45\ 	ext{m}$$ high, how long does it take for the projectile to hit the ground? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

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

Question 13

Which of the following is the correct vector addition rule?

Accepted Answer

Add corresponding components: $$	extbf{A} + 	extbf{B} = (A_x + B_x, A_y + B_y)$$

Question 14

A car moves with a velocity of $$20\ 	ext{m/s}$$ north and then turns east, moving at $$15\ 	ext{m/s}. $$What is the magnitude of the car's resultant velocity?

Accepted Answer

$$v = \sqrt{20^2$ + 15^2$} = \sqrt{400 + 225} = \sqrt{625} = 25\ 	ext{m/s}$$

Question 15

Which coordinate system is most appropriate for describing the motion of a planet around the Sun?

Accepted Answer

Polar coordinate system

Question 16

A car accelerates from $$10\ 	ext{m/s} to$$ $$30\ 	ext{m/s} in$$ $$5\ 	ext{s}. $$What is the average acceleration?

Accepted Answer

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

Question 17

A person walks 3 km east, then 4 km north. What is the total distance traveled and the magnitude of displacement?

Accepted Answer

Distance: $$3 + 4 = 7 km$$; Displacement: $$\sqrt{3^2$ + 4^2$} = 5 km$$

Question 18

A car moves along a straight road with a velocity given by $$v(t) = 5t. $$What is the displacement of the car from $$t = 0 to$$ $$t = 4 s$$?

Accepted Answer

$$\Delta x = \$$int_0$$^4 5t\ dt = \left.\frac{5}{2} t^2$ight|_0^4$ = \frac{5}{2} 	imes 16 = 40\ 	ext{m}$$

Question 19

Which of the following best describes instantaneous velocity?

Accepted Answer

The derivative of position with respect to time: $$v = \frac{dx}{dt}$$

PHYS 2211 Midterm 1: Study Guide and Exam Information

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