Physics Study Guide/Linear motion

From Wikibooks, open books for an open world
Jump to: navigation, search
Physics Study Guide (Print Version)
Units Linear Motion Force Momentum Normal Force and Friction Work Energy
Thermodynamics Electricity Magnetism Optics
Physical Constants Frictional Coefficients Greek Alphabet Logarithms Vectors and Scalars Other Topics








One dimensional coordinate system
Two dimensional coordinate system
Three dimensional coordinate system



Displacement answers the question, "Has the object moved?"

Note the \equiv symbol. This symbol is a sort of "super equals" symbol, indicating that not only does \vec x_f- \vec x_i EQUAL the displacement \Delta\vec{x}, but more importantly displacement is OPERATIONALLY DEFINED by \vec x_f- \vec x_i.


  1. Measure where the object is initially.
  2. Measure where the object is at some later time.
  3. Determine the difference between these two position values.

Be sure to note that DISPLACEMENT is NOT the same as DISTANCE travelled.











[δ is the lower-case delta.] Or with the idea of limits from calculus, we have ...







Again, also note that technically we have a definition for AVERAGE acceleration. As for displacement, if we are careful to use a series of small velocity changes, then we can write the definition for INSTANTANEOUS acceleration as


Or with the help of calculus, we have ...



Notice that the definitions given above for displacement, velocity, and acceleration included little arrows over many of the terms. The little arrow reminds us that direction is an important part of displacement, velocity, and acceleration. These quantities are VECTORS. By convention, the little arrow always points right when placed over a letter. So for example, \vec v just reminds us that velocity is a vector, and does NOT imply that this particular velocity is rightward. Why do we need vectors? As a simple example, consider velocity. It is not enough to know how fast one is moving. We also need to know which direction we are moving. Less trivially, consider how many different ways an object could be experiencing an acceleration (a change in its velocity). Ultimately there are three distinct ways an object could accelerate.

  1. The object could be speeding up.
  2. The object could be slowing down.

(More general accelerations are simply combinations of 1 and 3 or 2 and 3).

Importantly, a change in the direction of motion is just as much an acceleration as is speeding up or slowing down. In classical mechanics, no direction is associated with time (you cannot point to next Tuesday). So the definition of \vec a_{av} tells us that acceleration will point wherever the CHANGE in velocity \Delta\vec{v} points. Understanding that the direction of \Delta \vec{v} determines the direction of \vec a leads to three non-mathematical but very powerful rules of thumb.

  3. If the velocity and acceleration of an object are perpendicular to each other, the object's initial speed stays constant (in that initial direction), while the speed of the object in the direction of the acceleration increases--think of a bullet fired horizontally in a vertical gravitational field. Since velocity in the one direction remains constant, and the velocity in the other direction increases, the overall velocity (absolute velocity) also increases.

(Again, more general motion is simply a combination of 1 and 3 or 2 and 3.)


Equations of motion : Constant acceleration[edit]


 \frac{d \vec v}{dt} = 0\ \mathrm{m\ s^{-2}}



Giving the following equation for velocity as a function of time.




Integrating again gives the equation for position.


The following are the 'Equations of Motion'. They are simple and obvious equations if you think over them for a while.

Equations of Motion
Equation Description
 v^2 = v_0^2 + 2\vec{a}\cdot(\vec{x}-\vec{x}_0) \ Eliminating time (Very useful, see the section on Energy)
Key to Symbols
Symbol Description
\vec{v} velocity at time t
\vec{v_0} initial velocity
\vec{a} acceleration (constant)
t\ time taken during the motion
\vec{x} position at time t
\vec{x_0} initial position

Acceleration in One Dimension[edit]

Acceleration in Two Dimensions[edit]

(Needs content)

Acceleration in Three Dimensions[edit]

(Needs content)

Force in motion

We need force in our life and motion too because there are things which needs to have force while it is moving, and if there is no force and there is motion in an object, then the object won't move. If it was the opposite the result will be the same.

What does force in motion mean?[edit]


How do we calculate?[edit]




What is velocity?[edit]

It is not just the speed which is important when you go on a journey. The direction matters as well, then when you want to talk about direction as well as a speed we use the word velocity. This equation for the velocity is using the distance travelled, average speed and time taken. So it will be the same.

Those two racers are in a high speed while racing each other, they are stable in their direction, because they are in high speed and if the direction went out of control slightly and they are in high speed, then maybe the cyclist will get injured.



How do we calculate it?[edit]





This is the way you are going to calculate.

Observing motion[edit]



Measuring acceleration[edit]


Who is Newton, and what did he observe?[edit]

He was an English physicist, mathematician, astronomer, alchemist, and natural philosopher, he has three laws for physics, and they are:

  1. Newton's First Law (also known as the Law of Inertia) states that an object at rest tends to stay at rest and that an object in uniform motion tends to stay in uniform motion unless acted upon by a net external force.
  2. Newton's Second Law states that an applied force, F, on an object equals the time rate of change of its momentum, p. the acceleration of an object is directly proportional to the magnitude of the net force acting on the object and inversely proportional to its mass. In the MKS system of measurement, mass is given in kilograms, acceleration in metres per second squared, and force in newtons (named in his honour).
  3. Newton's Third Law states that for every action there is an equal and opposite reaction.


Distance travelled=D

Force= F

Initial velocity=U

Final velocity=V



Change in velocity=∆V



Gravity= G



Now here we are going to learn how to calculate the force, mass and acceleration. When we want to calculate the force, and we have the mass and acceleration, how are we going to calculate it? force=mass multiply acceleration This is considered in the second law of Newton. What is mass? Sometimes it is defined as the amount of matter in a body. But in Newton’s second law is defined as a numerical measure of inertia. What is inertia? The tendency of a body to maintain is state of rest or uniform motion unless acted upon by an external force.

Who is Hooke, and what is his law? (July 18, 1635 – March 3, 1703.)He was an English polymath who played an important role in the scientific revolution, through both experimental and theoretical work. His law was about the spring limit, if you have stretched the spring beyond its limit, it will then change permanently, and will not return to its original place. The rubber band doesn’t obey Hooke’s law. This spring is not beyond its limit, so when you remove the weight, then it will automatically return to its place.
