I Used to Know That_ Stuff You Forgot From School - Caroline Taggart [31]
☞ EQUATIONS OF MOTION
These are basic equations that describe the motion of a body moving with constant acceleration.
A body moving with constant acceleration (a) starts with an initial velocity (u) and achieves a final velocity (v) in a time of t seconds, covering a total distance s. If you know any three of these components, you can decipher the other two.
Acceleration can be expressed as
Distance traveled (s) is simply time multiplied by average speed:
These two equations—one for calculating acceleration and the other for calculating distance—are essentially all that is known here, but some other equations can be obtained by combining them.
For example, eliminate v from both of them. The first equation can be recast as
v = u + at
(multiply everything by t, then add u to both sides) and the second as:
(multiply everything by 2, divide by t, and deduct u from both sides).
This may sound complicated, but the point is to produce an equation that defines v. Just in case you want to calculate v, you understand.… But you also now have two equations beginning “v=,” so you can put them together and deduce that:
which, after a bit of rearranging, is equivalent to
s = ut + ½at2.
This looks a bit more impressive, but it’s not really telling you anything new.
Similarly, you could eliminate u from each of our original equations, yielding:
s = vt - ½at2.
Or eliminate t from them both to show that:
v2 = u2 + 2as.
So, to give an example, if a body traveling at 30 m/sec (u) accelerates at 2 m/sec/sec (a) for 10 sec (t), it reaches a velocity (v):
v = at + u = (2x10) + 30 = 50 meters per second
s = ut + ½at2 = (30 x 10)+(½ x 2 x 102)
= 300 + 100 = 400 meters.
Average speed is distance traveled (s) divided by t, which in this instance is = 40 m/sec. Which sounds reasonable, because it starts at 30 and ends up at 50.
Apparently, this isn’t rocket science, unless you have a rate of acceleration equal to the force of gravity, in which case you are into the realm of projectiles and ballistics, which is, um, rocket science.
HISTORY
High-school history books are typically gargantuan tomes of no fewer than 1,500 pages. You probably never covered more than 10 chapters or so, but you still had to lug those monstrous compilations onto the bus each day. Today, with history just a click away, students can quickly locate a specific historical tidbit or surf for hours (or even days) collecting information on major historical events.
With thousands of years to cover, and many choices and opinions regarding the proper texts, this chapter can only scratch the surface. But one thing most people agree upon regarding history is the importance of its study. As writer and philosopher George Santayana stressed so insightfully, “Those who cannot remember the past are condemned to repeat it.”
Notable U.S. Presidents
At the time of publication, there have been 44 presidents of the United States. Since there is not enough room to include a compete list, what follows are facts about some of the most notable ones, with their time in office noted following their name. (D = Democrat, R = Republican—parties that came into being around 1828 and 1854, respectively.)
George Washington (1789-97): commander-in-chief of the forces that rebelled against British rule in the 1770s, and president of the Constitutional Convention of 1787, which produced the blueprint of today’s Constitution. Unanimously elected first President of the United States two years later. Probably didn’t chop down a cherry tree or tell his father that he couldn’t tell a lie, but the legend persists.
John Adams (1797-1801): another major figure in the War of Independence, known as the “colossus of the debate” over the Declaration of Independence.