The DISPLACEMENT, D x is the change from one position to another, i.e., D x= x 2 -x 1 . Positive values of D x represent motion in the positive direction (increasing values of x , i.e. left to right looking into the page), while negative values correspond to decreasing x. x =.
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another, i.e., Dx= x2-x1. Positive values of Dx represent motion in
the positive direction (increasing values of x, i.e. left to right looking
into the page), while negative values correspond to decreasing x.
-3 -2 -1 0 1 2 32: Motion in a Straight Line
Position and Displacement.
To locate the position of an object we need to define this RELATIVE
to some fixed REFERENCE POINT, which is often called the
In the one dimensional case (i.e. a straight
line), the origin lies in the middle of an
AXIS (usually denoted as the ‘x’-axis)
which is marked in units of length.
Note that we can also define
NEGATIVE co-ordinates too.
Displacement is a VECTOR quantity. Both its size (or ‘magnitude’)
AND direction (i.e. whether positive or negative) are important.
We can describe the position of an
object as it moves (i.e. as a function
of time) by plotting the x-position
of the object (Armadillo!) at different
time intervals on an (x , t) plot.
The average SPEED is simply the
total distance travelled (independent
of the direction or travel) divided by
the time taken. Note speed is a
SCALAR quantity, i.e., only its
magnitude is important (not its
From HRW p15
by the displacement (Dx) divided
by the time taken for this
displacement to occur (Dt).
The SLOPE of the (x,t) plot gives average VELOCITY.
Like displacement, velocity is a
VECTOR with the same sign as
The INSTANTANEOUS VELOCITY
is the velocity at a specific
moment in time, calculated by making
Dt infinitely small (i.e., calculus!)
is given by a, where,
SI unit of acceleration is
metres per second squared (m/s2)
Acceleration is a change in
velocity (Dv) in a given time (Dt).
The average acceleration, aav,
is given by
that the acceleration is a
constant, we can derive a set
of equations in terms of the
Constant Acceleration and the Equations of Motion
For some types of motion (e.g., free
fall under gravity) the acceleration
is approximately constant, i.e., if
v0 is the velocity at time t=0, then
Usually in a given problem, three of these quantities are given
and from these, one can calculate the other two from the following
equations of motion.
At the surface of the earth, neglecting any effect due to air resistance
on the velocity, all objects accelerate towards the centre of earth
with the same constant value of acceleration.
This is called FREE-FALL ACCELERATION, or ACCELERATION
DUE TO GRAVITY, g.
At the surface of the earth, the magnitude of g = 9.8 ms-2
Note that for free-fall, the equations of motion are in the y-direction
(i.e., up and down), rather than in the x direction (left to right).
Note that the acceleration due to gravity is always towards the centre
of the earth, i.e. in the negative direction, a= -g = -9.8 ms-2
initial position is y0=0 and
at the max. height vm a x=0
Therefore, time to max height from
A man throws a ball upwards with an initial velocity of 12ms-1.
(a) how long does it take the ball to reach its maximum height ?
(b) what’s the ball’s maximum height ?
release point ?
Note that there are TWO SOLUTIONS here (two different ‘roots’ to
the quadratic equation). This reflects that the ball passes the same
point on both the way up and again on the way back down.