Tru Physics

Chapter 6: Constant Acceleration

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6.1 Introduction to Constant Acceleration Motion

Constant acceleration is an important concept in physics that describes the motion of an object that experiences a steady (unchanging) increase or decrease in velocity over time. This type of motion is also known as uniformly accelerated motion, as the object’s velocity changes by a constant amount during each equal time interval.

One of the key properties of constant acceleration is that it produces a linear relationship between an object’s velocity and time. This corresponds to a quadratic (parabolic) relation between position and time.

As mentioned in the previous chapter, physics is all about understanding the physical conditions at play. Thus, when writing down the equations in this chapter, be sure to keep in mind the primary condition here. That is, these equations are valid for situations in which there is constant acceleration. In other words, the acceleration of the object does not change with time.

6.2 Constant Acceleration Equations

The following kinematic equations are essential when solving problems involving constant acceleration.

x_f=x_i + v_{i,x}t+ \dfrac{1}{2} a_x t^2

v_{f,x} = v_{i,x} + a_x t

v_{f,x}^2 = v_{i,x}^2 + 2 a_x \Delta x

\Delta x = \dfrac{1}{2}\left(v_{i,x}+v_{f,x}\right)\Delta t

Note that the third equation says nothing about the time of motion (t). This can be extremely useful when solving problems that don’t provide any information about the time during which the motion takes place.

6.3 Acceleration Due to Gravity

When discussing constant acceleration, we always start with acceleration due to gravity which is a crucial and intuitive example of this type of motion. Acceleration due to gravity is the rate at which objects fall toward the Earth due to the pull of gravity. This type of acceleration is a constant that affects all objects on earth, regardless of their mass or size.

Gravity affects all objects, from feathers to hammers, and from apples to space stations. Constant acceleration
Gravity affects all objects, from feathers to hammers, and from apples to space stations.

The conventional standard for the acceleration due to gravity is given as:

g = 9.80665 \dfrac{\text{m}}{\text{s}^2}.

However, this value will vary slightly depending on one’s location on Earth. Thus, most physicists will simplify the value to 9.8 \frac{\text{m}}{\text{s}^2} or even 10 \frac{\text{m}}{\text{s}^2} depending on the accuracy needed. This expression represents the change in velocity per second that an object will experience as it falls toward the Earth. It is important to understand that Earth is not special in this concept of acceleration due to gravity. Objects on other planets experience gravity as well. The acceleration due to gravity takes on a different constant value for each of the celestial objects below:

  • Mercury: 3.7 \frac{\text{m}}{\text{s}^2}
  • Venus: 8.87 \frac{\text{m}}{\text{s}^2}
  • Earth’s Moon: 1.62 \frac{\text{m}}{\text{s}^2}
  • Mars: 3.71 \frac{\text{m}}{\text{s}^2}
  • Jupiter: 24.79 \frac{\text{m}}{\text{s}^2}
  • Saturn: 10.44 \frac{\text{m}}{\text{s}^2}
  • Uranus: 8.87 \frac{\text{m}}{\text{s}^2}
  • Neptune: 11.15 \frac{\text{m}}{\text{s}^2}
  • Pluto: 0.58 \frac{\text{m}}{\text{s}^2}

Please note that these values may vary slightly based on the specific location on each planet, but they provide a good general estimate.

It is also important to note that acceleration due to gravity only acts in one direction: downward. This means that objects will fall towards the earth with a constant acceleration of 9.8 \frac{\text{m}}{\text{s}^2}, unless acted upon by another force, such as air resistance.

The concept of acceleration due to gravity is crucial in understanding a wide range of physical phenomena, including projectile motion which we will study in chapter 11. By understanding acceleration due to gravity, we can make predictions about the motion of objects in projectile motion problems.

6.4 The Myth of Zero Gravity

Contrary to popular belief, astronauts do not experience “zero gravity.” Instead, they are in a state of weightlessness, which is caused by being in a state of free fall toward the planet they are orbiting. Although they appear to float, they are actually being pulled toward the planet by its gravitational field. Astronauts aboard the International Space Station, for example, are falling toward the Earth at a rate of 9.8 \frac{\text{m}}{\text{s}^2}, which is the same rate at which objects fall to Earth’s surface due to its gravitational pull. However, because they are continuously falling, they do not hit the surface, and instead continue to orbit the planet. This continuous state of free fall gives the illusion of being weightless, but the astronauts are still being influenced by the gravitational field of the planet.

The International Space Station (ISS) is in constant free fall toward earth due to the force of gravity. Constant acceleration.
The International Space Station (ISS) is in constant free fall toward earth due to the force of gravity.

Acceleration due to gravity is a fundamental concept in physics that helps us understand how objects fall towards the earth and the motion of projectiles. It provides us with the tools to make predictions about the motion of objects and to solve a wide range of problems in physics.

Chapter Summary

This chapter looked into the concept of constant acceleration, describing the motion of an object whose velocity steadily increases or decreases over time. This uniformly accelerated motion results in a linear relationship between velocity and time and a quadratic relationship between position and time. We discussed the case of acceleration due to gravity which affects all objects on Earth. This principle extends to other celestial bodies, each having its own unique gravitational acceleration. Interestingly, astronauts in orbit experience continuous free fall rather than zero gravity, creating the illusion of weightlessness. We also introduced kinematic equations to calculate the position, velocity, and change in position of an object experiencing constant acceleration.

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Quiz 3 is also available and covers content from Chapters 5 and 6. Enroll in the Canvas course using the link above if you haven’t already. Then, click here to take the quiz.

Knowledge Check

Answer the quiz questions below.

How does constant acceleration affect an object’s motion over time?
It causes the object to stop.
Incorrect, constant acceleration does not cause an object to stop. Instead, it describes a situation where an object’s velocity increases or decreases at a constant rate over time.
It makes the object move at a constant speed.
Incorrect, constant acceleration does not cause an object to move at a constant speed. It results in a steady change in the object’s velocity over time.
It results in a steady change in the object’s velocity over time.
Correct! Constant acceleration is when an object’s velocity changes at a constant rate over time, causing a linear relationship between velocity and time, and a quadratic relationship between position and time.
How does the concept of acceleration due to gravity relate to the motion of falling objects on Earth?
Objects fall at different rates depending on their mass.
Incorrect, according to the principle of equivalence, all objects fall at the same rate in the absence of air resistance. The acceleration due to gravity is a constant that affects all objects on earth, regardless of their mass or size.
Gravity pulls objects upwards.
Incorrect, gravity always acts downwards, pulling objects towards the center of the Earth. This downward force results in a constant acceleration as objects fall towards Earth.
Gravity causes objects to fall towards Earth with a constant acceleration.
Correct! The acceleration due to gravity causes objects to fall towards the Earth at a constant rate, affecting all objects equally regardless of their mass or size.
How do gravity values differ across various celestial bodies like Mars, Jupiter, or the Moon?
The gravity values are the same across all celestial bodies.
Incorrect, gravity values vary across celestial bodies. Each planet or moon has its own unique gravitational acceleration due to its unique mass and size.
The gravity values are highest on the smallest celestial bodies.
Incorrect, the size of a celestial body is not directly related to its gravity. Gravity depends on both the mass of the celestial body and the distance from its center.
Each celestial body has its own unique gravitational acceleration.
Correct! The gravity value of a celestial body depends on its mass and size. Thus, each planet or moon has a different acceleration due to gravity.
Why do astronauts appear to experience “zero gravity” when they are in space?
Because there is no gravity in space.
Incorrect, gravity exists everywhere in space. Astronauts appear to be weightless not because there is no gravity, but because they are in a state of continuous free fall towards the Earth.
Because the spaceship shields them from gravity.
Incorrect, the spaceship does not shield astronauts from gravity. They appear to be weightless because they are in a state of continuous free fall, orbiting the planet.
Because they are in a state of continuous free fall.
Correct! Astronauts in space are actually in a state of continuous free fall towards the Earth, which gives the illusion of zero gravity or weightlessness.
How are the kinematic equations used in the context of constant acceleration motion?
They are used to calculate the mass of the object.
Incorrect, the kinematic equations are not used to calculate mass. Instead, they are used to calculate quantities such as final position, final velocity, and change in position of an object undergoing constant acceleration.
They are used to determine the direction of motion.
Incorrect, while kinematic equations do include vector quantities, they don’t inherently determine direction. They are used to calculate position, velocity, and change in position of an object experiencing constant acceleration.
They are used to calculate the position, velocity, and change in position of an object undergoing constant acceleration.
Correct! The kinematic equations are used to calculate the final position, final velocity, and change in position of an object undergoing constant acceleration.
Continue to Chapter 7: Forces
Back to Chapter 5: Constant Velocity

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