Gravity (on earth): 9. 81 meters/second2 Speed of light: 3 × 108 meters/second Molar gas constant: 8. 32 Joules/(mole × Kelvin) Avogadro’s number: 6. 02 × 1023 per mole Planck’s Constant: 6. 63 × 10-34 Joules × seconds
Velocity = Change in position/Change in time (v=dx/dt) Acceleration = Change in velocity/Change in time (a=dv/dt) Current velocity = Initial velocity + (Acceleration × time) (v=v0+a×t) Force = Mass × acceleration (F=m×a) Kinetic energy = (1/2)Mass × velocity2 (K=(1/2)m×v) Work = Displacement × force (W=d×F) Power = Change in work/Change in time (P=dW/dt) Momentum = Mass × velocity (p=m×v)
For example, let’s look at a very simple equation: Acceleration = Change in velocity/Change in time,[3] X Research source or a = Delta(v)/Delta(t). Acceleration is the force that causes an object’s velocity to change. If an object has an initial velocity of v0 at time t0 and a final velocity of v at time t, the object can be said to accelerate as it changes from v0 to v. Acceleration can’t be instantaneous — no matter how fast it occurs, there will be some time difference between when the object is traveling at its initial velocity and when it reaches its final velocity. Thus, a = (v - v0/t - t0) = Delta(v)/Delta(t).
Pre-algebra and algebra (for basic equations and “find the unknown” problems) Trigonometry (for force diagrams, rotation problems, and angled systems) Geometry (for problems dealing with area, volume, etc. ) Precalculus and calculus (for taking derivatives and integrals of physics equations — usually advanced topics) Linear algebra (for calculations involving vectors — usually advanced topics).
For example, let’s say that we need to find the acceleration that a car experiences as its velocity changes over two seconds. If the car weighs 1,000 kilograms, starts moving at 9 m/s and ends at 22 m/s, we can say that v0 = 9 m/s, v = 22 m/s, m = 1,000 t = 2 s. As noted above, the standard acceleration equation is a = (v - v0/t - t0). Note that this doesn’t take the object’s mass into account, so we can ignore the fact that the car weighs 1,000 kg. Thus, we would solve as follows: a = (v - v0/t - t0) = ((22 - 9)/(2 - 0)) = (13/2) = 6. 5 m/s2
Mass: Grams or kilograms Force: Newtons Velocity: meters/second (sometimes kilometers/hour) Acceleration meters/second2 Energy/Work: Joules or kilojoules Power: Watts
For example, let’s say that a problem asks you to find the rate that a 5 kilogram wooden block accelerates along a smooth floor if pushed with a force of 50 newtons. Since F = m × a, the answer may seem to be as simple as solving for a in the equation 50 = 5 × a. However, in the real world, the force of friction will act against the forward motion of the object, effectively reducing the force it’s being pushed with. Leaving this out of the problem will result in an answer that has the block accelerating slightly faster than it actually would.
While simply re-doing your work is one way to check your math, you may also want to use common sense to relate your problem to real life as a way of checking your answer. For example, if you’re trying to find the momentum (mass × velocity) of an object moving in the forward direction, you wouldn’t expect a negative answer, since mass can’t be negative and velocity is only negative if it’s in the “negative” direction (i. e. , opposite the “forward” direction in your frame of reference). Thus, if you get a negative, answer, you’ve probably made an error in your calculations somewhere along the line.
If you have lingering questions after class, talk to your teacher. Try to make your questions as specific as possible — this shows the teacher that you were listening. If the teacher isn’t busy, she or he will probably be able to schedule an appointment to go over the material with you and help you understand it. You could even ask your professor or teacher if they would be willing to let you record the lectures so that you can listen to them again later. This would allow you to ask for clarification on anything that is still unclear to you after re-listening to the lecture.
If you’re not happy with your grade in physics, don’t be content to simply use the problems assigned in your homework for practice. Make the extra effort to complete problems you wouldn’t normally encounter — these can be problems in your textbook that aren’t assigned to you, free problems online, or even problems in physics practice books (usually sold at academic bookstores).
Your teacher (via after-school appointment) Your friends (via study groups and homework sessions) Tutors (either privately-hired or as part of a school program) Third-party resources (like physics problem books, educational sites like Khan Academy, and so on)
