$$R = \frac{v_0$^2 \sin 2\theta}{g}$$

Question 1

A car accelerates from rest at a constant rate $$a$$ for a time $$t. $$What is the final velocity $$v of $$the car?

Accepted Answer

$$v = v_0$ + at$$

Question 2

Which equation correctly relates displacement $$x to $$initial velocity $$v_0$$, acceleration $$a$$, and time $$t$$?

Accepted Answer

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

Question 3

A ball is thrown vertically upward with an initial velocity $$v_0. $$What is the maximum height $$h it $$reaches?

Accepted Answer

$$h = \frac{v_0$^2}{2g}$$

Question 4

Which formula gives the centripetal acceleration $$a_c$$ for an object moving in a circle of radius $$r at $$speed $$v$$?

Accepted Answer

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

Question 5

A block slides down a frictionless incline of height $$h. $$What is its speed $$v at $$the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 6

Which equation represents Newton's Second Law for a net force $$F$$ acting on a mass $$m$$?

Accepted Answer

$$F = ma$$

Question 7

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the formula for its range $$R$$?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g}$$

Question 8

Which equation gives the gravitational force $$F_g$$ between two masses $$m_1$$ and $$m_2$$ separated by distance $$r$$?

Accepted Answer

$$F_g = G \frac{m_1$ m_2$}{r^2$}$$

Question 9

A spring with spring constant $$k is $$compressed by distance $$x. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$

Question 10

Which equation gives the period $$T of a $$simple pendulum of length $$L$$?

Accepted Answer

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Question 11

A rotating disk has angular velocity $$\omega$$ and moment of inertia $$I. $$What is its rotational kinetic energy?

Accepted Answer

$$K = \frac{1}{2} I \$$omega^2$$

Question 12

A force $$F is $$applied at a distance $$r$$ from the axis of rotation. What is the torque $$	au$$ produced?

Accepted Answer

$$	au = r F \sin 	heta$$

Question 13

Which equation gives the work $$W$$ done by a constant force $$F$$ over a displacement $$d at $$angle $$	heta$$?

Accepted Answer

$$W = F d \cos 	heta$$

Question 14

A mass $$m$$ moves at velocity $$v. $$What is its kinetic energy $$K$$?

Accepted Answer

$$K = \frac{1}{2} m v^2$

Question 15

Which equation gives the impulse $$J$$ delivered by a force $$F$$ over time $$\Delta t$$?

Accepted Answer

$$J = F \Delta t$$

Question 16

A satellite orbits Earth in a circular path of radius $$r. $$What is its orbital speed $$v$$?

Accepted Answer

$$v = \sqrt{\frac{GM}{r}}$$

Question 17

Which equation gives the frequency $$f of a $$wave with speed $$v$$ and wavelength $$\lambda$$?

Accepted Answer

$$f = \frac{v}{\lambda}$$

Question 18

A block of mass $$m is $$attached to a spring and oscillates with angular frequency $$\omega. $$What is the period $$T of $$oscillation?

Accepted Answer

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

Question 19

Which equation gives the mechanical advantage (MA) of a lever with input arm length $$l_{in}$$ and output arm length $$l_{out}$$?

Accepted Answer

$$MA = \frac{l_{in}}{l_{out}}$$

PH101 Final Test Formula Sheet – Core Physics Equations and Constants

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