Studying uniformly accelerated rectilinear motion

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Badanie ruchu jednostajnie przyspieszonego prostoliniowego

You will learn

how to study uniformly accelerated rectilinear motion,
how to study uniformly accelerated rectilinear motion using English vocabulary.

Exercise 1

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nagranie abstraktu

Answer the questions.

1. How do we define an accelerated motion?
2. How do we define uniformly accelerated rectilinear motion?
3. Give an example of uniformly accelerated rectilinear motion.

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Motion of the body on an inclined plane

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Experiment

Experiment 1

Research problem

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nagranie abstraktu

Studying motion of the cart on an inclined planeinclined planeinclined plane.

Hypothesis

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nagranie abstraktu

Movement of the cart on an inclined plane is a uniformly accelerated motion.

You will need

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nagranie abstraktu

1. inclined planeinclined planeinclined plane about 2 m long (e.g. wooden board),
2. cart,
3. stopwatch,
4. ruler or measuring tape,
5. paper tape.

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nagranie abstraktu

Instruction

1. Place the inclined plane on the laboratory table (inclination angle: 15°, length: minimum 1,6 m).
2. Put the paper tape along an inclined plane.
3. Place the cart at the top of the inclined plane and let it roll.
4. At regular intervals (every 1 s), mark the position of the cart on the paper tape.
5. Measure the length of the sections covered by the cart (marked on the paper tape).
6. Record the results in the measurement table.


$s [m]$
$t [s]$
$Δ s [m]$
$Δ t [s]$
$v_{a v} = \frac{Δ s}{Δ t} [\frac{m}{s}]$
$Δ v_{a v} [\frac{m}{s}]$
$a = \frac{Δ v_{a v}}{Δ t} [\frac{m}{s^{2}}]$

Hint

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nagranie abstraktu

1. Time is measured similarly to the distance measurement, i.e. from the beginning of the body motion. Since the distance travelled is measured every second, the following time values should be: 1 s, 2 s, 3 s, etc.
2. Δs is the distance between consecutive body positions read from the table above.
3. Time is measured every 1 second, so the Δt value is always 1 s.
4. The average speed of a moving body is calculated by dividing the distance and time interval (Δt = 1 s).
5. The average speed changes are calculated as the difference of its subsequent values. If, on the other hand, we divide them over a period of time, equal to 1 s, we will obtain the value of the accelerationaccelerationacceleration of the cart rolling down the inclined planeinclined planeinclined plane.

Elaboration of results

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nagranie abstraktu

1. Calculate the accelerationaccelerationacceleration for each measurement:

a = \frac{Δ v}{Δ t} = \frac{v_{f} - v_{i}}{t_{f} - t_{i}}

where:
vIndeks dolny f - final speed,
vIndeks dolny i Indeks dolny koniec- initial speed,
Δt - time interval,
tIndeks dolny f - final time,
tIndeks dolny i - initial time.

If we assume that before the body begins to move, it is at rest ( $v_{o} = 0$ ), then after transforming the above formula, we get:

v_{f} = a \cdot Δ t

2. Compare the results.
3. Check how much the speed of the cart increases at equal time intervals.
4. Draw a conclusion from the experiment.

Summary

Observation

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nagranie abstraktu

The cart speed increases by the same amount at successive identical time intervals.

Conclusions

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nagranie abstraktu

- The acceleration with which the cart moved was constant, i.e. it did not change during body motion.
- The motion of the cart is a uniformly accelerated rectilinear motionuniformly accelerated rectilinear motion.
- The speed increases by the same amount at identical time intervals (e.g. every second), and the trajectory of motion is a straight linestraight linestraight line.

Exercise 2

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nagranie abstraktu

Determine if the sentences below are true or false.

a) In a uniformly accelerated motion, the speed of the body increases linearly.
b) The final velocityvelocityvelocity for $v_{o} = 0$ is calculated from the formula $v_{f} = a \cdot Δ t$ .
c) The unit of accelerationaccelerationacceleration may be $\frac{k m}{s^{2}}$ , $\frac{k m}{h^{2}}$ .

Exercise 3

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nagranie abstraktu

The body moves with an accelerationaccelerationacceleration of 4 $\frac{m}{s^{2}}$ . What speed will it reach after 15 seconds? Select the correct answer.

a) 3,74 $\frac{m}{s}$

b) 60 $\frac{k m}{h}$

c) 3,75 $\frac{k m}{h}$

d) 60 $\frac{m}{s}$

Summary

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nagranie abstraktu

The uniformly accelerated rectilinear motiouniformly accelerated rectilinear motion is a motion in which the acceleration is constant. This means that the speed increases by a constant value at identical time intervals (e.g. every second), and the trajectory of motion is a straight linestraight linestraight line.
The final speed, which the body, having the initial speed $v_{o} = 0$ , reached in uniformly accelerated rectilinear motion, we can determine from the formula:
$v_{f} = a \cdot Δ t$
where:
vIndeks dolny f $[\frac{m}{s}]$ - final speed of the body,
a $[\frac{m}{s^{2}}]$ - accelerationaccelerationacceleration of the body,
Δt - the time interval in which the body moved with the specified acceleration.
Characteristic of the uniformly accelerated rectilinear motionuniformly accelerated rectilinear motion is the uniform increase of the speed of the moving body by a constant value at the same time intervals.

Exercises

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Exercise 4

The elevator moves with an acceleration of 0,9 $\frac{m}{s^{2}}$ . When will it reach the speed of 1,5 $\frac{m}{s}$ starting from rest?

1,667 s
1,766 s
1,765 s
1,350 s

zadanie

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Exercise 5

Determine the average magnitude of acceleration of a cyclist riding a bicycle and when driving on a slope of terrain during time t = 10 s he changed his speed from $v_{i} = 18 \frac{k m}{h}$ to the speed $v_{f} = 54 \frac{k m}{h}$ . Assume that the cyclist's motion is a uniformly accelerated rectilinear motion. Give the result in $\frac{m}{s^{2}}$ .

$v_{i} = 18 \frac{k m}{h} = \frac{18 \cdot 1000 m}{3600 s} = 5 \frac{m}{s}$

$v_{f} = 54 \frac{k m}{h} = \frac{54 \cdot 1000 m}{3600 s} = 15 \frac{m}{s}$

$a = \frac{v_{f} - v_{i}}{Δ t} = \frac{15, 0 \frac{m}{s} - 5 \frac{m}{s}}{10 s} = 1 \frac{m}{s^{2}}$

$a = 1 \frac{m}{s^{2}}$

Exercise 6

Write in English what type of motion the falling apple moves and with what magnitude of acceleration.

It is a uniformly accelerated motion. The acceleration magnitude is 9,81 $\frac{m}{s^{2}}$ , it is the value of gravitational acceleration of Earth, g.

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Exercise 7

Indicate which pairs of expressions or words are translated correctly.

ruch jednostajnie przyspieszony prostoliniowy - uniformly accelerated rectilinear motion
równia pochyła - inclined plane
linia prosta - straight line
szybkość zmiany prędkości - rate of change of velocity
prędkość - acceleration
przyspieszenie - velocity

zadanie

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Match Polish terms with their English equivalents.

acceleration
linia prosta
prędkość
przyspieszenie
szybkość zmiany prędkości
inclined plane
rate of change of velocity
straight line
równia pochyła
velocity

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Glossary

acceleration

przyspieszenie

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wymowa w języku angielskim: acceleration

inclined plane

równia pochyła

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wymowa w języku angielskim: inclined plane

rate of change of velocity

szybkość zmiany prędkości

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wymowa w języku angielskim: rate of change of velocity

straight line

linia prosta

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wymowa w języku angielskim: straight line

uniformly accelerated rectilinear motion

ruch jednostajnie przyspieszony prostoliniowy

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wymowa w języku angielskim: uniformly accelerated rectilinear motion

velocity

prędkość

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wymowa w języku angielskim: velocity

Keywords

accelerationaccelerationacceleration

inclined planeinclined planeinclined plane

uniformly accelerated rectilinear motionuniformly accelerated rectilinear motion

velocityvelocityvelocity

Scenariusz

Summary

Exercises

Glossary

Keywords