Uniform rectilinear motion
A train travelling along a straight track without changing speed. A baggage conveyor belt. A lift that always rises in the same way. They all have something in common: they move in a straight line without speeding up or slowing down. This kind of motion has its own name.
What URM is
If you watch a bubble rising up a vertical tube of oil and note down its height every second ($0\ \text{s} \rightarrow 0\ \text{cm}$, $1\ \text{s} \rightarrow 4\ \text{cm}$, $2\ \text{s} \rightarrow 8\ \text{cm}$, $3\ \text{s} \rightarrow 12\ \text{cm}$), you will see that it covers identical distances in equal times: how do we define and describe this very regular motion mathematically?
Explain in your own words what uniform motion in a straight line (MRU) is: what is its trajectory like? What is its speed like?
Explain in your own words what uniform motion in a straight line (MRU) is: what is its trajectory like? What is its speed like?
Which of these motions can be a MRU? Justify your answers. a) A train travelling along a straight track at $120\ \text{km/h}$ without changing its speed. b) A car stuck…
Which of these motions can be a MRU? Justify your answers.
- a) A train travelling along a straight track at $120\ \text{km/h}$ without changing its speed.
- b) A car stuck in a traffic jam.
- c) A luggage conveyor belt that turns on curves.
- d) A lift ascending at a constant speed.
Measuring every second, a car travels $10\ \text{m}$ in the first second, $15\ \text{m}$ in the second second and $20\ \text{m}$ in the third second. a) Is it uniform…
Measuring every second, a car travels $10\ \text{m}$ in the first second, $15\ \text{m}$ in the second second and $20\ \text{m}$ in the third second.
- a) Is it uniform motion in a straight line? Why?
- b) What is its average speed during those $3\ \text{s}$?
The URM equation
Move the sliders for the initial position $x_0$ and the speed $v$ and see how the line on the $x(t)$ graph changes: the equation above updates with the values you choose.
An object moving with MRU covers $5\ \text{m}$ every second. a) How many metres does it cover in $4\ \text{s}$? b) And in $10\ \text{s}$?
An object moving with MRU covers $5\ \text{m}$ every second.
- a) How many metres does it cover in $4\ \text{s}$?
- b) And in $10\ \text{s}$?
A construction hoist rises at $0,5\ \text{m/s}$. How long does it take to get from the ground to scaffolding $12\ \text{m}$ high?
A construction hoist rises at $0,5\ \text{m/s}$. How long does it take to get from the ground to scaffolding $12\ \text{m}$ high?
An object passes through the positions $x = 0\ \text{m}$, $4\ \text{m}$, $8\ \text{m}$ and $12\ \text{m}$ at times $t = 0\ \text{s}$, $1\ \text{s}$, $2\ \text{s}$ and…
An object passes through the positions $x = 0\ \text{m}$, $4\ \text{m}$, $8\ \text{m}$ and $12\ \text{m}$ at times $t = 0\ \text{s}$, $1\ \text{s}$, $2\ \text{s}$ and $3\ \text{s}$, as shown in the figure.
- a) What distance does it cover each second?
- b) What is its speed? Is it a MRU?
- c) If it continues like this, what position will it be at time $t = 10\ \text{s}$?
Meeting and chasing
Two cyclists leave at the same time, one from each village, along the straight $24\ \text{km}$ road connecting them. One travels at $15\ \text{km/h}$ and the other at…
Two cyclists leave at the same time, one from each village, along the straight $24\ \text{km}$ road connecting them. One travels at $15\ \text{km/h}$ and the other at $9\ \text{km/h}$, as shown in the figure.
- a) At what speed do they approach each other?
- b) How long does it take for them to meet?
- c) What distance has each travelled when they meet?
Leo sets off walking along a straight path at $1,5\ \text{m/s}$. Sixty seconds later Nora sets off along the same path at $3\ \text{m/s}$, as shown in the figure (at the…
Leo sets off walking along a straight path at $1,5\ \text{m/s}$. Sixty seconds later Nora sets off along the same path at $3\ \text{m/s}$, as shown in the figure (at the moment Nora sets off).
- a) How much of a head start does Leo have at the moment Nora sets off?
- b) How many metres does Nora gain on Leo each second?
- c) How long does it take Nora to catch up with him?