Q: Given the position vector $$\vec{r}(t) = (6.0t - 0.10t^2$)\hat{i} + (8.0t - 0.000025t^3$)\hat{j}$$ for a sports car on a winding road, what is the car's speed at $$t = 120\ \text{s}$$?

$$\sqrt{(-18)^2$ + (-33)^2$} = 38\ \text{m/s}$$

Q: A spacecraft initially drifts north at $$680\ \text{m/s}$$, then accelerates at $$75\ \text{m/s}^2 at an $$angle $$25^\circ$$ north of east. What is the $$x-$$component of its acceleration?

$$75 \cos 25^\circ = 68.0\ \text{m/s}^2$$

Q: A police car fires a bullet at $$300\ \text{m/s}$$ while driving at $$50\ \text{m/s}. $$What is the bullet's speed as measured by a stationary TV camera?

$$300\ \text{m/s} + 50\ \text{m/s} = 350\ \text{m/s}$$

Q: A plane flies east at $$500\ \text{mph}$$, but a wind blows south at $$50\ \text{mph}. $$What is the plane's ground speed?

$$\sqrt{500^2$ + 50^2$} = 502\ \text{mph}$$

Q: A ceiling fan spinning at $$60\ \text{rpm}$$ coasts to a stop in $$25\ \text{s}. $$How many revolutions does it make while stopping?

$$\frac{79}{2\pi} = 12.6\ \text{cycles}$$

Question 1

Given the position vector $$\vec{r}(t) = (6.0t - 0.10t^2$)\hat{i} + (8.0t - 0.000025t^3$)\hat{j}$$ for a sports car on a winding road, what is the car's speed at $$t = 120\ 	ext{s}$$?

Accepted Answer

$$\sqrt{(-18)^2$ + (-33)^2$} = 38\ 	ext{m/s}$$

Question 2

A spacecraft initially drifts north at $$680\ 	ext{m/s}$$, then accelerates at $$75\ 	ext{m/s}^2 at an $$angle $$25^\circ$$ north of east. What is the $$x-$$component of its acceleration?

Accepted Answer

$$75 \cos 25^\circ = 68.0\ 	ext{m/s}^2$$

Question 3

For projectile motion, what is the equation for the $$y-$$position as a function of $$x$$?

Accepted Answer

$$y(x) = -\frac{1}{2}\frac{g}{v_{x,0}^2}x^2$ + \frac{v_{y,0}}{v_{x,0}}x$$

Question 4

A bow-and-arrow hunter shoots at a coconut that falls at the exact instant the arrow is released. Will the arrow hit the coconut?

Accepted Answer

Yes, because both the arrow and coconut experience the same vertical acceleration due to gravity.

Question 5

A police car fires a bullet at $$300\ 	ext{m/s}$$ while driving at $$50\ 	ext{m/s}. $$What is the bullet's speed as measured by a stationary TV camera?

Accepted Answer

$$300\ 	ext{m/s} + 50\ 	ext{m/s} = 350\ 	ext{m/s}$$

Question 6

A plane flies east at $$500\ 	ext{mph}$$, but a wind blows south at $$50\ 	ext{mph}. $$What is the plane's ground speed?

Accepted Answer

$$\sqrt{500^2$ + 50^2$} = 502\ 	ext{mph}$$

Question 7

In uniform circular motion, what is the expression for the tangential velocity?

Accepted Answer

$$v = r \omega$$

Question 8

What is the period $$T of an $$object in uniform circular motion with angular velocity $$\omega$$?

Accepted Answer

$$T = \frac{2\pi}{\omega}$$

Question 9

A ceiling fan spinning at $$60\ 	ext{rpm}$$ coasts to a stop in $$25\ 	ext{s}. $$How many revolutions does it make while stopping?

Accepted Answer

$$\frac{79}{2\pi} = 12.6\ 	ext{cycles}$$

Question 10

For nonuniform circular motion, what is the angular acceleration $$\alpha if $$the angular velocity changes from $$\omega_i to$$ $$\omega_f in $$time $$\Delta t$$?

Accepted Answer

$$\alpha = \frac{\omega_f - \omega_i}{\Delta t}$$

Question 11

What is the magnitude of the centripetal acceleration for an object moving in a circle of radius $$r$$ with speed $$v$$?

Accepted Answer

$$a_c = \frac{v^2$}{r}$$

Question 12

If an object in circular motion has both radial and tangential acceleration components, what is the total acceleration magnitude?

Accepted Answer

$$|a| = \sqrt{a_r^2$ + a_t^2$}$$

Question 13

In projectile motion, what launch angle $$	heta$$ gives the maximum range for a given initial speed $$v_0$$?

Accepted Answer

$$	heta = 45^\circ$$

Question 14

Which component of acceleration changes the magnitude of velocity in 2D motion?

Accepted Answer

The parallel component $$a_{\parallel}(t)$$

Question 15

Which component of acceleration changes the direction of velocity in 2D motion?

Accepted Answer

The perpendicular component $$a_{\perp}(t)$$

Question 16

If Bill moves at $$15\ 	ext{m/s}$$ away from Amy, and Carlos moves at $$5\ 	ext{m/s}$$ relative to Amy, what is Carlos' velocity relative to Bill?

Accepted Answer

$$v_{CB} = v_{CA} - v_{AB} = 5\ 	ext{m/s} - 15\ 	ext{m/s} = -10\ 	ext{m/s}$$

Question 17

For a plane flying east at $$500\ 	ext{mph}$$ with a wind blowing south at $$50\ 	ext{mph}$$, where is the plane after $$0.6$$ hours?

Accepted Answer

$$(300, -30)\ 	ext{miles}$$

Question 18

In uniform circular motion, what is the relationship between angular velocity $$\omega$$ and frequency $$f$$?

Accepted Answer

$$\omega = 2\pi f$$

Physics I: Mechanics – Kinematics in 2D, Projectile Motion, Relative Motion, and Circular Motion – Step-by-Step Study Guidance

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