You're riding the Metro in Mexico City and, on a straight stretch, the train moves along without speeding up or slowing down. Or think of the baggage belt at the airport, which always moves the suitcases the same way. That very regular motion has its own name and is the simplest to describe. How do you calculate where something moving like this will be?
What is URM
Imagine a bubble rising through a tube of oil. You write down its height every second: $0\ \text{s} \rightarrow 0\ \text{cm}$, $1\ \text{s} \rightarrow 4\ \text{cm}$, $2\ \text{s} \rightarrow 8\ \text{cm}$, $3\ \text{s} \rightarrow 12\ \text{cm}$. It covers equal distances in equal times. What is this motion called, and how is it described?
So, if you know the speed, you can find how far it travels in any amount of time: $d = v \times t$. And also how long it takes: $t = \dfrac{d}{v}$.
Practice★☆☆Not started
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.
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 $3\ \text{s}$?
A cyclist goes down a mountain pass at $72\ \text{km/h}$. a) Express their speed in $\text{m/s}$. b) What distance do they cover in $15\ \text{s}$ at that speed?
A cyclist goes down a mountain pass at $72\ \text{km/h}$.
a) Express their speed in $\text{m/s}$.
b) What distance do they cover in $15\ \text{s}$ at that speed?
So far we have measured how far something travels. But what if the object doesn't start at the origin? Then it's useful to say where it is at each instant.
Why? The final position is where it started ($x_0$) plus how far it moved ($v \times t$).
Move the sliders for the initial position $x_0$ and the speed $v$: the line on the $x(t)$ graph changes. If you increase $v$, the line gets steeper.
Practice★☆☆Not started
An object moving with MRU covers $5\ \text{m}$ every second. a) How many meters 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 meters does it cover in $4\ \text{s}$?
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 $t = 10\ \text{s}$?
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 meters does Nora gain on Leo each second?
c) How long does it take Nora to catch up with him?
Have you ever walked on an escalator in the Metro and gone faster? Your speed depends on relative to what you measure it.
Practice★★★Not started
An escalator ascends at $0.5\ \text{m/s}$, as shown in the figure. a) If you walk up it at $1\ \text{m/s}$ relative to the steps, at what speed are you ascending…
An escalator ascends at $0.5\ \text{m/s}$, as shown in the figure.
a) If you walk up it at $1\ \text{m/s}$ relative to the steps, at what speed are you ascending relative to the shopping center floor?
b) What if you walk down at $1\ \text{m/s}$ while the escalator is ascending? In which direction are you moving relative to the floor?
c) What would happen if you walked down at $0.5\ \text{m/s}$? Explain each case.
At the gym, the treadmill displays $12\ \text{km/h}$. a) How many meters does a runner "cover" in $5\ \text{min}$ on the treadmill? b) Has she changed position relative…
At the gym, the treadmill displays $12\ \text{km/h}$.
a) How many meters does a runner "cover" in $5\ \text{min}$ on the treadmill?
b) Has she changed position relative to the gym floor? Explain the difference between motion relative to the treadmill and relative to the floor.
Problems with more than one leg or with great distances
The same ideas solve problems about trips and even about light.
Practice★★☆Not started
Between two villages there are $30\ \text{km}$ of straight road. a) How long does a car travelling at $60\ \text{km/h}$ take? Give the answer in hours and in minutes. b)…
Between two villages there are $30\ \text{km}$ of straight road.
a) How long does a car travelling at $60\ \text{km/h}$ take? Give the answer in hours and in minutes.
b) At what speed would it have to travel to take only $20\ \text{min}$?
A family can go to the beach via two routes: by motorway, $120\ \text{km}$ at $100\ \text{km/h}$, or by main road, $90\ \text{km}$ at $60\ \text{km/h}$. a) Calculate the…
A family can go to the beach via two routes: by motorway, $120\ \text{km}$ at $100\ \text{km/h}$, or by main road, $90\ \text{km}$ at $60\ \text{km/h}$.
a) Calculate the time they take for each route, in hours.
b) Express those times in minutes.
c) Which route gets them there faster? How many minutes difference is there?
A fishing boat sails in a straight line at $10\ \text{km/h}$ for $3\ \text{h}$. a) How far from the port is it? b) At what speed must it return to be back in…
A fishing boat sails in a straight line at $10\ \text{km/h}$ for $3\ \text{h}$.
a) How far from the port is it?
b) At what speed must it return to be back in $2\ \text{h}$?
c) What is the average speed for the whole trip, there and back?