Topicm1f72958090baaade_1528449000663_0Topic

Studying uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion

Levelm1f72958090baaade_1528449084556_0Level

Second

Core curriculumm1f72958090baaade_1528449076687_0Core curriculum

III. Planning and conducting observations or experiments and inference based on their results.

II. 7) The student names a uniformly accelerated motion – a motion in which the speed increases in unit time intervals by the same amount, and a uniformly decelerated motion - a motion in which the speed decreases in unit time intervals by the same amount.

Timingm1f72958090baaade_1528449068082_0Timing

45 minutes

General learning objectivesm1f72958090baaade_1528449523725_0General learning objectives

Experimental study of uniformly accelerated rectilinear motion.

Key competencesm1f72958090baaade_1528449552113_0Key competences

1. Defining uniformly accelerated rectilinear motion.

2. Determining dependencies between quantities describing the studied motion.

3. Developing skills of conducting experiments independently.

Operational (detailed) goalsm1f72958090baaade_1528450430307_0Operational (detailed) goals

The student:

- defines uniformly accelerated motion,

- experimentally determines the quantities describing this motion.

Methodsm1f72958090baaade_1528449534267_0Methods

1. Learning by experimenting.

2. Learning by solving empirical problems.

Forms of workm1f72958090baaade_1528449514617_0Forms of work

1. Individual work while performing experiments.

2. Group work - solving research problems.

Lesson stages

Introductionm1f72958090baaade_1528450127855_0Introduction

Task 1

Answer the questions:

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

Answer:

1. Accelerated motion is a motion in which the speed changes over time.
2. Uniformly accelerated rectilinear motion is a motion in which the speed increases in unit time intervals by the same amount and the trajectory is a straight linestraight linestraight line.
3. An example of a uniformly accelerated rectilinear motion can be a free fall of a steel ball under the influence of the Earth's gravitational force.

Procedurem1f72958090baaade_1528446435040_0Procedure

[Interactive graphics]

Experiment 1

Research problem:

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

Hypothesis:

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

What will be needed:

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

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 1s), 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.m1f72958090baaade_1527752256679_01. 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 1s), 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.

[Table 1]

Hints:

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:

1. Calculate the acceleration for each measurement:

where:
vIndeks dolny f_f - final speed,
vIndeks dolny i_i - initial speed,
Δt - time interval,
tIndeks dolny f_f - final time,
tIndeks dolny i_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:

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.

Observation:

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

Conclusions:

- 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 motion.
- The speed increases by the same amount at identical time intervals (e.g. every second), and the trajectory of motion is a straight line.m1f72958090baaade_1527752263647_0- 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 motion.
- The speed increases by the same amount at identical time intervals (e.g. every second), and the trajectory of motion is a straight line.

Task 2

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 $v_f=a·∆t$.
c) The unit of accelerationaccelerationacceleration may be $\frac{{\displaystyle km}}{s^2}$, $\frac{{\displaystyle km}}{h^2}$.

Answer:

a) True. b) True. c) True.

Task 3

Select the correct answer:

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

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

b) 60 $\frac{{\displaystyle km}}{h}$

c) 3,75 $\frac{{\displaystyle km}}{h}$

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

Answer:

a) False. b) False. c) False. d) True.

Lesson summarym1f72958090baaade_1528450119332_0Lesson summary

The uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly 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:

where:
vIndeks dolny f_f $\left[\frac{m}{s}\right]$ - final speed of the body,
a $\left[\frac{m}{s^2}\right]$ - 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 motionuniformly accelerated rectilinear motion is the uniform increase of the speed of the moving body by a constant value at the same time intervals.

Selected words and expressions used in the lesson plan

accelerationaccelerationacceleration

inclined planeinclined planeinclined plane

rate of change of velocityrate of change of velocityrate of change of velocity

straight linestraight linestraight line

uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion

velocityvelocityvelocity