Acceleration
A car pulling away from traffic lights does not always travel at the same speed: it gains a little more with every second. This quantity, how quickly velocity changes, is acceleration. Going fast is not the same as accelerating a lot, and learning to tell them apart is the key to this section.
What acceleration is
You look at the speedometer of a motorbike as it sets off in a straight line: at $0\ \text{s}$ it reads $0\ \text{m/s}$, at $1\ \text{s}$ it reads $4\ \text{m/s}$, at $2\ \text{s}$ it reads $8\ \text{m/s}$ and at $3\ \text{s}$ it reads $12\ \text{m/s}$. How can we measure, with a single quantity, the rate at which this velocity changes?
The speedometer of the train you are travelling on shows an increasing speed as it leaves the station. Explain in your own words what acceleration is and which two…
The speedometer of the train you are travelling on shows an increasing speed as it leaves the station. Explain in your own words what acceleration is and which two physical quantities it relates to time.
A car has an acceleration of $3\ \text{m/s}^2$. Explain what this value means: by how much does its speed increase each second? If it starts from rest, what speed will…
A car has an acceleration of $3\ \text{m/s}^2$. Explain what this value means: by how much does its speed increase each second? If it starts from rest, what speed will it have after $4\ \text{s}$?
A skater starts from rest and reaches $10\ \text{m/s}$ in $5\ \text{s}$. Calculate their acceleration using $a = \frac{\Delta v}{\Delta t}$ and state its unit.
A skater starts from rest and reaches $10\ \text{m/s}$ in $5\ \text{s}$. Calculate their acceleration using $a = \frac{\Delta v}{\Delta t}$ and state its unit.
Acceleration and braking: interpreting the signs
A car brakes and goes from $20\ \text{m/s}$ to a standstill in $4\ \text{s}$. Calculate its acceleration. Why is the result negative?
A car brakes and goes from $20\ \text{m/s}$ to a standstill in $4\ \text{s}$. Calculate its acceleration. Why is the result negative?
A tram travelling at $72\ \text{km/h}$ brakes to a standstill in $8\ \text{s}$. Express the initial speed in $\text{m/s}$ and calculate the braking acceleration.
A tram travelling at $72\ \text{km/h}$ brakes to a standstill in $8\ \text{s}$. Express the initial speed in $\text{m/s}$ and calculate the braking acceleration.
Two cars carry out an emergency stop from $30\ \text{m/s}$: the first comes to a stop in $6\ \text{s}$ and the second in $4\ \text{s}$, as shown in the graph. Calculate…
Two cars carry out an emergency stop from $30\ \text{m/s}$: the first comes to a stop in $6\ \text{s}$ and the second in $4\ \text{s}$, as shown in the graph.
Calculate the acceleration of each car and explain which of the two brakes more intensely.
The acceleration due to gravity: free fall
If you drop a rubber and a heavy book at the same time from the same height, you find that both hit the floor together. Why do they fall at the same rate if the Earth pulls much harder on the heavier object?
In free fall, with no air resistance, the speed of an object increases by $9,8\ \text{m/s}$ every second. What speed does a stone falling for $3\ \text{s}$ have? What is…
In free fall, with no air resistance, the speed of an object increases by $9,8\ \text{m/s}$ every second. What speed does a stone falling for $3\ \text{s}$ have? What is this acceleration called, and which letter is used to represent it?
A ball is dropped from a bridge, with negligible air resistance. Taking $g = 9,8\ \text{m/s}^2$, what speed does it have after $2\ \text{s}$ of falling? And after…
A ball is dropped from a bridge, with negligible air resistance. Taking $g = 9,8\ \text{m/s}^2$, what speed does it have after $2\ \text{s}$ of falling? And after $3,5\ \text{s}$?
You drop a coin from the top of a tower. Calculate its speed after $1\ \text{s}$, $2\ \text{s}$, and $4\ \text{s}$ of falling ($g = 9,8\ \text{m/s}^2$), and explain the…
You drop a coin from the top of a tower. Calculate its speed after $1\ \text{s}$, $2\ \text{s}$, and $4\ \text{s}$ of falling ($g = 9,8\ \text{m/s}^2$), and explain the pattern you observe in the results.
Going fast is not the same as accelerating a lot
A car goes from $0$ to $20\ \text{m/s}$ in $10\ \text{s}$ and a motorbike goes from $0$ to $12\ \text{m/s}$ in $3\ \text{s}$. Calculate the acceleration of each vehicle.…
A car goes from $0$ to $20\ \text{m/s}$ in $10\ \text{s}$ and a motorbike goes from $0$ to $12\ \text{m/s}$ in $3\ \text{s}$. Calculate the acceleration of each vehicle. Which one accelerates more, even if the car ends up travelling faster?
A car pulls away at traffic lights: it accelerates from rest for $5\ \text{s}$ up to $15\ \text{m/s}$, maintains that speed for a while, and then brakes until it stops…
A car pulls away at traffic lights: it accelerates from rest for $5\ \text{s}$ up to $15\ \text{m/s}$, maintains that speed for a while, and then brakes until it stops in $3\ \text{s}$, as shown in the graph.
- a) Calculate the acceleration when pulling away.
- b) What is the acceleration while it maintains its speed? Why?
- c) Calculate the braking acceleration and compare it with the acceleration when pulling away.
Marcos states: "the car travelling faster is the one with greater acceleration". Analyse whether he is right using these data: car A goes from $0$ to $25\ \text{m/s}$ in…
Marcos states: "the car travelling faster is the one with greater acceleration". Analyse whether he is right using these data: car A goes from $0$ to $25\ \text{m/s}$ in $10\ \text{s}$ and car B goes from $0$ to $20\ \text{m/s}$ in $4\ \text{s}$, as shown in the graph.
- a) Calculate the acceleration of each car as it pulls away.
- b) Which one is going faster at the end? Which one has accelerated more?
- c) Explain in your own words the difference between "going fast" and "accelerating a lot".