Q: A car travels 15 yards. Convert this distance into meters. (1 yard = 3 feet, 1 foot = 12 inches, 1 inch = 2.54 cm, 100 cm = 1 m)

$$15 \times 3 \times 12 \times 2.54 \div 100 = 13.716$$ meters

Q: A truck travels up a frictionless incline with an initial velocity of $$24.6\ \mathrm{m/s}$$ and an acceleration of $$-6.44\ \mathrm{m/s^2$}. $$What is the truck’s velocity at $$t = 0.71\ \mathrm{s}$$?

$$v = 24.6 + (-6.44) \times 0.71 = 20.03\ \mathrm{m/s}$$

Q: A planet orbits its sun in a circle of radius $$1.61 \times 10$$^{11}$$ m, making one revolution in 1.18$$ \times $$10^8 s. $$What is the planet’s tangential speed?

$$v = \frac{2\pi r}{T} = \frac{2\pi \times 1.61 \times 10$$^{11}$$}{1.18 \times 10^8$} = 8.58 \times 10^3$\ \mathrm{m/s}$$

Q: A home has $$2400$$ square feet. Convert this area to square inches. (1 foot = 12 inches)

$$2400 \times (12)^2$ = 345600$$ square inches

Question 1

A car travels 15 yards. Convert this distance into meters. (1 yard = 3 feet, 1 foot = 12 inches, 1 inch = 2.54 cm, 100 cm = 1 m)

Accepted Answer

$$15 	imes 3 	imes 12 	imes 2.54 \div 100 = 13.716$$ meters

Question 2

How many significant figures are in the measurement 0.004520 m?

Accepted Answer

4

Question 3

Given the kinematic equation $$y_f = y_i + v_i t + \frac{1}{2} a t^2$, solve for a$.

Accepted Answer

$$a = \frac{2(y_f - y_i - v_i t)}{t^2$}$$

Question 4

A truck travels up a frictionless incline with an initial velocity of $$24.6\ \mathrm{m/s}$$ and an acceleration of $$-6.44\ \mathrm{m/s^2$}. $$What is the truck’s velocity at $$t = 0.71\ \mathrm{s}$$?

Accepted Answer

$$v = 24.6 + (-6.44) 	imes 0.71 = 20.03\ \mathrm{m/s}$$

Question 5

Refer to the first image (Displacement vs. Time). What is the velocity of the object between $$t = 0$$ and $$t = 4$$ seconds?

Accepted Answer

$$v = \frac{8\ \mathrm{m} - 0\ \mathrm{m}}{4\ \mathrm{s} - 0\ \mathrm{s}} = 2\ \mathrm{m/s}$$

Question 6

For the velocity vs. time graph in the third image, what is the acceleration between $$t = 10 s $$and $$t = 15 s$$?

Accepted Answer

$$a = \frac{-6 - 2}{15 - 10} = \frac{-8}{5} = -1.6\ \mathrm{m/s^2$}$$

Question 7

A bird can travel at $$19\ \mathrm{m/s} in $$still air. There is a $$10\ \mathrm{m/s}$$ wind blowing east. How fast is the bird traveling relative to the ground if it flies eastward?

Accepted Answer

$$19 + 10 = 29\ \mathrm{m/s}$$

Question 8

Suppose a tornado launches a car at an angle of $$64^\circ$$ with a speed of $$51\ \mathrm{m/s}. $$What is the car’s initial vertical velocity ($$v_y$$)?

Accepted Answer

$$v_y = 51 \sin 64^\circ = 45.8\ \mathrm{m/s}$$

Question 9

A planet orbits its sun in a circle of radius $$1.61 	imes 10$$^{11}$$ m, making one revolution in 1.18$$ 	imes $$10^8 s. $$What is the planet’s tangential speed?

Accepted Answer

$$v = \frac{2\pi r}{T} = \frac{2\pi 	imes 1.61 	imes 10$$^{11}$$}{1.18 	imes 10^8$} = 8.58 	imes 10^3$\ \mathrm{m/s}$$

Question 10

Refer to the fourth image (Position vs. Time, upward curve). What does the shape of this graph indicate about the object’s acceleration?

Accepted Answer

The object has a constant, nonzero acceleration.

Question 11

A home has $$2400$$ square feet. Convert this area to square inches. (1 foot = 12 inches)

Accepted Answer

$$2400 	imes (12)^2$ = 345600$$ square inches

Question 12

Given vectors $$\vec{A} = 50\ \mathrm{m/s} at$$ $$30^\circ$$ south of east and $$\vec{B} = 40\ \mathrm{m/s} at$$ $$80^\circ$$ south of west, what is the $$x-$$component of $$\vec{A}$$?

Accepted Answer

$$A_x = 50 \cos 30^\circ = 43.3\ \mathrm{m/s}$$

Question 13

For the first image (Displacement vs. Time), what is the object’s acceleration between $$t = 8 s $$and $$t = 10 s$$?

Accepted Answer

The acceleration is negative (deceleration), as the slope of the displacement curve is decreasing.

Question 14

A car is launched at $$51\ \mathrm{m/s} at$$ $$64^\circ$$ above the horizontal. What is the car’s horizontal velocity ($$v_x$$)?

Accepted Answer

$$v_x = 51 \cos 64^\circ = 22.4\ \mathrm{m/s}$$

Question 15

What is the average velocity of an object that moves from $$x = 0 m to$$ $$x = 10 m in$$ $$5$$ seconds?

Accepted Answer

$$v_{avg} = \frac{10 - 0}{5 - 0} = 2\ \mathrm{m/s}$$

Graphical Kinematics: Analyzing Position, Velocity, and Acceleration from Graphs

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