Non-Uniform Motion and Average Speed

Flashcards covering concepts of non-uniform motion, trajectory types, average speed calculations, graph analysis, sample problems, and historical contributions of Borys Paton.

What is the definition of non-uniform motion?

Non-uniform motion is motion during which a body covers different distances in equal intervals of time, meaning its speed changes with time.

How is mechanical motion classified according to the shape of its trajectory?

It is classified into rectilinear motion (the trajectory is a straight line) and curvilinear motion (the trajectory is a curved line).

How is mechanical motion classified according to the character of the body's motion over time?

It is classified into uniform motion (the speed value does not change with time) and non-uniform motion (the speed value changes with time).

What is the physical definition and formula for average speed ($v_{\text{avg}}$) in non-uniform motion?

Average speed is a physical quantity equal to the ratio of the total distance $l$ covered by a body to the time interval $t$ during which this distance was covered: $v_{\text{avg}} = \frac{l}{t}$.

In the formula for average speed, what does the time interval $t$ include?

The time interval $t$ is the sum of the time the body spent moving plus any time spent on stops during that motion.

If a train covers a distance of $150\,\text{km}$ between two stations in $2.5\,\text{h}$, what is its average speed?

Its average speed is $v_{\text{avg}} = \frac{150\,\text{km}}{2.5\,\text{h}} = 60\,\text{km/h}$.

How is the distance $l_1$ calculated from a velocity-time graph when a body accelerates uniformly from $0$ to $20\,\text{m/s}$ over $15\,\text{s}$?

It is determined by calculating the area of the shaded triangle: $l_1 = \frac{1}{2} \times (20\,\text{m/s} \times 15\,\text{s}) = \frac{300\,\text{m}}{2} = 150\,\text{m}$.

If a body travels uniformly at $20\,\text{m/s}$ for $10\,\text{s}$, what distance $l_2$ does it cover?

The distance covered is $l_2 = 20\,\text{m/s} \times 10\,\text{s} = 200\,\text{m}$.

What is the average speed of a body that covers a total distance of $350\,\text{m}$ in $25\,\text{s}$?

The average speed is $v_{\text{avg}} = \frac{350\,\text{m}}{25\,\text{s}} = 14\,\text{m/s}$.

Why can a distance-time graph never slope downward?

Because covered distance cannot decrease; therefore, the distance-time graph either rises or stays horizontal, but never descends.

A boy rides a bicycle for $1.5\,\text{h}$ at $20\,\text{km/h}$ and then walks the remaining $1\,\text{km}$ on foot in $0.5\,\text{h}$. What was his average speed on the entire journey?

The average speed was $v_{\text{avg}} = \frac{l_1 + l_2}{t_1 + t_2} = \frac{(20\,\text{km/h} \times 1.5\,\text{h}) + 1\,\text{km}}{1.5\,\text{h} + 0.5\,\text{h}} = \frac{31\,\text{km}}{2\,\text{h}} = 15.5\,\text{km/h}$.

What was the boy's walking speed $v_2$ when walking the last $1\,\text{km}$ in $0.5\,\text{h}$?

His walking speed was $v_2 = \frac{l_2}{t_2} = \frac{1\,\text{km}}{0.5\,\text{h}} = 2\,\text{km/h}$.

When and where was Borys Yevhenovych Paton born?

He was born in 1918 in Kyiv.

What research and achievements brought worldwide fame to Borys Paton?

His research in the field of electric arc welding and the creation of automatic welding machines used in industry and construction.

In what year did Borys Paton become the director of the E. O. Paton Electric Welding Institute in Kyiv?

In 1953.

What major metallurgical method was developed under the leadership of Borys Paton to enhance quality?

The electroslag process (електрошлаковий процес).

In what year was Borys Paton elected a full member of the Academy of Sciences of Ukraine, and from which year did he serve as its president?

He was elected a full member in 1958 and served as its president starting in 1962.