This is about how things move in a straight line or more scientifically how things move in

one dimension. This is useful for learning how to describe the movement of cars along a straight

road or of trains along straight railway tracks. If you want to understand how any object moves,

for example a car on the freeway, a soccer ball being kicked towards the goal or your dog chasing

the neighbour’s cat, then you have to understand three basic ideas about what it means when

something is moving. These three ideas describe different parts of exactly how an object moves.

They are:

1. position or displacement which tells us exactly where the object is,

2. speed or velocity which tells us exactly how fast the object’s position is changing or more

familiarly, how fast the object is moving, and

3. acceleration which tells us exactly how fast the object’s velocity is changing.

You will also learn how to use position, displacement, speed, velocity and acceleration to describe

the motion of simple objects. You will learn how to read and draw graphs that summarise the

motion of a moving object. You will also learn about the equations that can be used to describe

motion and how to apply these equations to objects moving in one dimension.

**Distance a****nd Displacement**** **

**Definition: Displacement**

Displacement is the change in an object’s position. The displacement of an object is defined as its change in position (final position minus initial position). Displacement has a magnitude and direction and is therefore a vector. For example, if the initial position of a car is xi and it moves to a final position of xf , then the displacement is:

xf − xi

However, subtracting an initial quantity from a final quantity happens often in Physics, so we

use the shortcut ∆ to mean final – initial. Therefore, displacement can be written:

∆x = xf − xi

**Important:** The symbol ∆ is read out as delta. ∆ is a letter of the Greek alphabet and is

used in Mathematics and Science to indicate a change in a certain quantity, or a final value

minus an initial value. For example, ∆x means change in x while ∆t means change in t.

**Important:** The words initial and final will be used very often in Physics. Initial will always

refer to something that happened earlier in time and final will always refer to something

that happened later in time. It will often happen that the final value is smaller than the

initial value, such that the difference is negative. This is ok!

**Definition: Vectors and Scalars**

A vector is a physical quantity with magnitude (size) and direction. A scalar is a physical

quantity with magnitude (size) only.

**The differences between distance and displacement can be summarised as:**

Distance

1. depends on the path

2. always positive

3. is a scalar

Displacement

1. independent of path taken

2. can be positive or negative

3. is a vector

**Speed, Average Velocity and Instantaneous Velocity**

**Definition: Velocity**

Velocity is the rate of change of position.

**Definition: Instantaneous velocity**

Instantaneous velocity is the velocity of an accelerating body at a specific instant in time.

**Definition: Average velocity**

Average velocity is the total displacement of a body over a time interval.

Velocity is the rate of change of position. It tells us how much an object’s position changes in

time. This is the same as the displacement divided by the time taken. Since displacement is a

vector and time taken is a scalar, velocity is also a vector. We use the symbol v for velocity. If

we have a displacement of ∆x and a time taken of ∆t, v is then defined as:

velocity (in m · s−1 ) =

v = change in displacement (in m) / change in time (in s) or = ∆x / ∆t

Velocity can be positive or negative. Positive values of velocity mean that the object is moving

away from the reference point or origin and negative values mean that the object is moving

towards the reference point or origin.

**Important:** An instant in time is different from the time taken or the time interval. It

is therefore useful to use the symbol t for an instant in time (for example during the 4th

second) and the symbol ∆t for the time taken (for example during the first 5 seconds of

the motion).

Average velocity (symbol v) is the displacement for the whole motion divided by the time taken

for the whole motion. Instantaneous velocity is the velocity at a specific instant in time.

(Average) Speed (symbol s) is the distance travelled (d) divided by the time taken (∆t) for

the journey. Distance and time are scalars and therefore speed will also be a scalar. Speed is

calculated as follows:

speed (in m · s−1 ) = distance (in m) / time (in s) or = d / ∆t

Instantaneous speed is the magnitude of instantaneous velocity. It has the same value, but no

direction.

**Differences between Speed and Velocity**

The differences between speed and velocity can be summarised as:

Speed

1. depends on the path taken

2. always positive

3. is a scalar

4. no dependence on direction and

so is only positive

Velocity

1. independent of path taken

2. can be positive or negative

3. is a vector

4. direction can be guessed from the sign (i.e. positive or negative)

Additionally, an object that makes a round trip, i.e. travels away from its starting point and then

returns to the same point has zero velocity but travels a non-zero speed.

**Acceleration **

**Definition: Acceleration**

Acceleration is the rate of change of velocity.

Acceleration (symbol a) is the rate of change of velocity. It is a measure of how fast the velocity

of an object changes in time. If we have a change in velocity (∆v) over a time interval (∆t),

then the acceleration (a) is defined as:

acceleration (in m · s−2 ) = change in velocity (in m · s−1 ) / change in time (in s)

a= ∆v / ∆t

Since velocity is a vector, acceleration is also a vector. Acceleration does not provide any infor-

mation about a motion, but only about how the motion changes. It is not possible to tell how

fast an object is moving or in which direction from the acceleration.

Like velocity, acceleration can be negative or positive. We see that when the sign of the acceler-

ation and the velocity are the same, the object is speeding up. If both velocity and acceleration

are positive, the object is speeding up in a positive direction. If both velocity and acceleration

are negative, the object is speeding up in a negative direction. If velocity is positive and accel-

eration is negative, then the object is slowing down. Similarly, if the velocity is negative and the

acceleration is positive the object is slowing down.

**Important:** Acceleration does not tell us about the direction of the motion. Acceleration

only tells us how the velocity changes.

**Important: Deceleration**

Avoid the use of the word deceleration to refer to a negative acceleration. This word usually

means slowing down and it is possible for an object to slow down with both a positive and

negative acceleration, because the sign of the velocity of the object must also be taken into

account to determine whether the body is slowing down or not.

eba ragalhuvey sir

gud

this post got; simulation and …./ can be taken anything out of these to the exam can’t u?

thanks for the hard work that u r doing,if study can pass all.

u r wc absee, if u put enough effort than there z no doubt abt passing..