The following topics are being discussed in this chapter:- Velocity
- Velocity as a vector
- Interesting formula 1
- Interesting formula 2
- Non-uniform motion
Velocity and acceleration - Physics - Theory - Entrance exam doctor and dentist
Linear motionIn 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 formulaThe 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.
ULMA motion following a straight line and with constant speed is called a uniform linear motion (ULM).
The graphs of a ULM look like this:
RemarkIn 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.
ReminderRemark: 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 m
Dt1 = 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.
VelocitySuppose 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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