Exercises: Acceleration

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 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 cyclist increases her speed from $6\ \text{m/s}$ to $16\ \text{m/s}$ in $5\ \text{s}$. What was her acceleration?

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?

Complete the sentence with the missing words: "Acceleration measures how fast the $\dots$ of a moving object changes, and in the International System of Units it is measured in $\dots$." Then give a numerical example.

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?

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 sports car goes from $0$ to $90\ \text{km/h}$ in $5\ \text{s}$. Express the final speed in $\text{m/s}$ and calculate the acceleration in $\text{m/s}^2$.

A bus goes from $36\ \text{km/h}$ to $72\ \text{km/h}$ in $5\ \text{s}$. Convert both speeds to $\text{m/s}$ and calculate its acceleration.

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 $3.5\ \text{s}$?

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 car accelerates at $2\ \text{m/s}^2$ while travelling at $5\ \text{m/s}$. How long does it take to reach $15\ \text{m/s}$?

A bicycle goes down a hill, gaining speed at a rate of $3\ \text{m/s}^2$ for $6\ \text{s}$. If it started at $2\ \text{m/s}$, what speed does it reach at the bottom of the hill?

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.

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.

A racing car goes from $0$ to $30\ \text{m/s}$ in $5\ \text{s}$ and, on reaching the bend, brakes from $30\ \text{m/s}$ to $10\ \text{m/s}$ in $4\ \text{s}$, as shown in the graph.

1. a) Calculate the acceleration in each phase.
2. b) In which phase is the acceleration greater in absolute value (without the sign)?
3. c) Explain the meaning of the sign of each acceleration.

A ballast bag is dropped from a stationary hot-air balloon, with negligible air resistance.

1. a) What speed does it have after $2\ \text{s}$ of falling? ($g = 9.8\ \text{m/s}^2$)
2. b) And after $5\ \text{s}$?
3. c) Your classmate says that, because it is heavy, the bag should fall with an acceleration greater than $9.8\ \text{m/s}^2$ even if there were no air. Are they right? Justify your answer.

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.

1. a) Calculate the acceleration when pulling away.
2. b) What is the acceleration while it maintains its speed? Why?
3. 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 $10\ \text{s}$ and car B goes from $0$ to $20\ \text{m/s}$ in $4\ \text{s}$, as shown in the graph.

1. a) Calculate the acceleration of each car as it pulls away.
2. b) Which one is going faster at the end? Which one has accelerated more?
3. c) Explain in your own words the difference between "going fast" and "accelerating a lot".

A rocket-powered sled starts from rest with an acceleration of $4\ \text{m/s}^2$ for $10\ \text{s}$.

1. a) What speed does it reach, in $\text{m/s}$?
2. b) Express it in $\text{km/h}$.
3. c) If it then brakes with an acceleration of $-2\ \text{m/s}^2$, how long does it take to come to a stop?

From the top of a cliff, a $100\ \text{g}$ stone and a $2\ \text{kg}$ stone are dropped at the same time, with negligible air resistance, as shown in the figure.

1. a) What speed does each stone have after $3\ \text{s}$ of falling? ($g = 9.8\ \text{m/s}^2$)
2. b) Which of the two reaches the ground first?
3. c) Explain why mass does not appear in these calculations.

An underground train accelerates from rest at $1.2\ \text{m/s}^2$ for $20\ \text{s}$, then travels at constant speed for $60\ \text{s}$, and brakes at $-0.8\ \text{m/s}^2$ until stopping at the next station.

1. a) What maximum speed does it reach?
2. b) How long does it take to brake from that speed?
3. c) How long does the entire journey between the two stations take?

We roll a ball down an inclined plane, as shown in the figure, and measure its speed every second: $0\ \text{m/s}$ on release, $1.5\ \text{m/s}$ after one second, $3\ \text{m/s}$ after two seconds, and $4.5\ \text{m/s}$ after three seconds.

1. a) Calculate its acceleration.
2. b) Predict what speed it will have after $6\ \text{s}$.
3. c) How would you experimentally test your prediction?