Practice problems and tests cannot possibly cover every situation that you may be asked to understand in physics. However, some categories of topics come up again and again, so much so that they might be worth some extra review. And that's exactly what these lessons are for - to give you a focused, intensive review of a few of the most essential physics topics.

Extra drill on difficult but frequently tested topics are:

- Tension Extra Drill Problems for AP Physics B & C
- Electric and Magnetic Fields Extra Drill Problems for AP Physics B & C
- Inclined Planes Extra Drill Problems for AP Physics B & C
- Motion Graphs Extra Drill Problems for AP Physics B & C
- Simple Circuits Extra Drill Problems for AP Physics B & C

We call them "drills" for a reason. They are designed to be skill-building exercises and as such, they stress repetition and technique. Working through these exercises might remind you of playing scales if you're a musician or of running laps around the field if you're an athlete. Not much fun, maybe a little tedious, but very helpufl in the long run.

The questions in each drill are all solved essentially the same way. Don't just do one problem after the other.....rather, do a couple, check to see that your answers are right, and then half an hour or a few days later, do a few more, just to remind yourself of the techniques involved.

Below are motion graphs problems.

### How to Do It

For a position–time graph, the slope is the velocity. For a velocity–time graph, the slope is the acceleration, and the area under the graph is the displacement.

### The Drill

Use the graph to determine something about the object's speed. Then play "Physics *Taboo*": suggest what object might reasonably perform this motion and explain in words how the object moves. Use everyday language. In your explanation, you *may not* use any words from the list below:

- velocity

- acceleration

- positive

- negative

- increase

- decrease

- it

- object

- constant

### The Answers

Note that our descriptions of the moving objects reflect our own imaginations. You might have come up with some very different descriptions, and that's fine … provided that your answers are conceptually the same as ours.

- The average speed over the first five seconds is 10 m/s, or about 22 mph. So:
- This motion only lasts 1 second, and the maximum speed involved is about 5 mph. So:
- The maximum speed of this thing is 30 cm/s, or about a foot per second. So:
- The steady speed over 200 s (a bit over 3 minutes) is 0.25 m/s, or 25 cm/s, or about a foot per second.
- The maximum speed here is 50 m/s, or over a hundred mph, changing speed dramatically in only 5 or 10 seconds. So:
- This thing covers 5 meters in 3 seconds, speeding up the whole time.
- Though this thing moves quickly—while moving, the speed is 1 m/s—the total distance covered is 1 mm forward, and 1 mm back; the whole process takes 5 ms, which is less than the minimum time interval indicated by a typical stopwatch. So we'll have to be a bit creative:
- Though this graph
*looks*like #7, this one is a velocity–time graph, and so indicates completely different motion. - This stuff moves 300 million meters in one second at a constant speed. There's only one possibility here: electromagnetic waves in a vacuum.
- Be careful about axis labels: this is an
*acceleration*–time graph. Something is accelerating at 1000 cm/s^{2}for a few seconds. 1000 cm/s^{2}= 10 m/s^{2}, about Earth's gravitational acceleration. Using kinematics, we calculate that if we drop something from rest near Earth, after four seconds the thing has dropped 80 m. - 1 cm/s is ridiculously slow. Let's use the world of slimy animals:
- This one looks a bit like those up-and-down-a-hill graphs, but with an important difference—this time the thing stops not just for an instant, but for five whole seconds, before continuing back toward the starting point.

Someone rolls a bowling ball along a smooth road. When the graph starts, the bowling ball is moving along pretty fast, but the ball encounters a long hill. So, the ball slows down, coming to rest after five seconds. Then, the ball comes back down the hill, speeding up the whole way.

A biker has been cruising up a hill. When the graph starts, the biker is barely moving at jogging speed. Within half a second, and after traveling only a meter up the hill, the bike turns around, speeding up as it goes back down the hill.

A toy racecar is moving slowly along its track. The track goes up a short hill that's about a foot long. After two seconds, the car has just barely reached the top of the hill, and is perched there momentarily; then, the car crests the hill and speeds up as it goes down the other side.

A cockroach crawls steadily along the school's running track, searching for food. The cockroach starts near the 50 yard line of the football field; around three minutes later, the cockroach reaches the goal line and, having found nothing of interest, turns around and crawls at the same speed back toward his starting point.

A small airplane is coming in for a landing. Upon touching the ground, the pilot puts the engines in reverse, slowing the plane. But wait! The engine throttle is stuck! So, although the plane comes to rest in five seconds, the engines are still on... the plane starts speeding up backwards! Oops …

An 8-year-old gets on his dad's bike. The boy is not really strong enough to work the pedals easily, so he starts off with difficulty. But, after a few seconds he's managed to speed the bike up to a reasonable clip.

In the Discworld novels by Terry Pratchett, wizards have developed a computer in which living ants in tubes, rather than electrons in wires and transistors, carry information. (Electricity has not been harnessed on the Discworld.) In performing a calculation, one of these ants moves forward a distance of 1 mm; stays in place for 3 ms; and returns to the original position. If this ant's motion represents two typical "operations" performed by the computer, then this computer has an approximate processing speed of 400 Hz times the total number of ants inside.

A small child pretends he is a bulldozer. Making a "brm-brm-brm" noise with his lips, he speeds up from rest to a slow walk. He walks for three more seconds, then slows back down to rest. He moved forward the entire time, traveling a total distance (found from the area under the graph) of 4 meters.

Light (or electromagnetic radiation of any frequency) is emitted from the surface of the moon. In 1 second, the light has covered about half the distance to Earth.

One way to simulate the effects of zero gravity is to drop an experiment from the top of a high tower. Then, because everything that was dropped is speeding up at the same rate, the effect is just as if the experiment were done in the Space Shuttle—at least until everything hits the ground. In this case, an experiment is dropped from a 250-ft tower, hitting the ground with a speed close to 90 mph.

A snail wakes up from his nap and decides to find some food. He speeds himself up from rest to his top speed in 10 seconds. During this time, he's covered 5 cm, or about the length of your pinkie finger. He continues to slide along at a steady 1 cm/s, which means that a minute later he's gone no farther than a couple of feet. Let's hope that food is close.

A bicyclist coasts to the top of a shallow hill, slowing down from cruising speed (–15 mph) to rest in 15 seconds. At the top, she pauses briefly to turn her bike around; then, she releases the brake and speeds up as she goes back down the hill.

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