| ## -## Jump to:The following topics are being discussed in this chapter: - Velocity- Velocity as a vector - Acceleration - Interesting formula 1 - Interesting formula 2 - Non-uniform motion |

## Slides transcription

# Velocity and acceleration - Physics - Theory - Entrance exam doctor and dentist

### Linear motion

In this chapter we will deal with linear motions.Here, a certain object moves from one position to another along a straight line.

We can present this on an axis and state that the object moves from position s1 to s2, and from time t1 to t2.

### Speed formula

The distance is s2 - s1 and we present it as Ds.Het time interval is t2 - t1 and we present it as Dt.

The speed with which the distance was covered, is given by:

So if the distance was 10.0 meter and it was done in 2.0 seconds, the speed was 5.0 m/s.

Not that this is the average speed.

It could have been higher at certain moments and lower at others, but on average it was 5.0 m/s.

### ULM

A motion following a straight line and with constant speed is called a uniform linear motion (ULM).The graphs of a ULM look like this:

### Remark

In order to work safely with our given data, we should convert them to standard SI-units (m for distance and length, kg for mass, s for time,…).De SI(standard)-unit for velocity is m/s.

If we have data in km/h, we convert it like this:

1 km/h = 1000 m / 3600 s = 1/3.6 m/s

1.0 m/s = 3.6 km/h (= 2.237 mi/h)

So to convert m/s to km/h we multiply by 3.6. In the opposite case we divide by 3.6.

### Reminder

Remark: the form a.b * 10n is called scientific notation.### Beware!

Beware with intuitive calculations with speeds!For example, suppose one rides 60 s at 4.0 m/s and then 60 s at 5.0 m/s.

What is the average speed for the complete ride?

Correct, 4.5 m/s:

Ds1 = 60 * 4.0 = 240 m and Ds2 = 60 * 5.0 = 300 m

Ds = Ds1 + Ds2 = 540 m

v = Ds / Dt = 540 / 120 = 4.5 m/s

But now this problem: someone rides 1000 m up a mountain at 4.0 m/s and goes down the other side 1000 m at 20 m/s, what is now the average speed?

Now the average speed for the full ride is NOT the average of the two speeds, so NOT 12 m/s!

### Beware!

The total distance Ds = 2000 mDt1 = Ds1 / v1 = 1000 / 4.0 = 250 s

Dt2 = Ds2 / v2 = 1000 / 20 = 50 s

The total time Dt = Dt1 + Dt2 = 250 + 50 = 300 s

v = Ds / Dt = 2000 / 300 = 6.6 m/s!

This is why mountain stages in the Tour de France have a lower average speed than flat stages.

### Velocity

Suppose we ride 200 m eastward and after that 100 m westward, all in 60 s. The covered distance is then 300 m and thus v = 300 m/ 60 s = 5.0 m/s.But the displacement is in fact only 100 m eastward: we rode 200 meter eastward and returned 100 m to arrive at 100 m from our starting point, and so the displacement is 100 m eastward and v = 100 m/60 s = 1.7 m/s.

So there are two “average speeds”: distance/time and displacement/time.

The first is called speed and is a scalar quantity.

E.g. the speed is 5.0 m/s.

The second is called velocity.

Velocity also has a direction, e.g. 1.7 m/s eastward. Velocity therefore is a vector, which we will now cover.

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