STD IX – MOTION IN ONE DIMENSION – ARCHIMEDES

MOTION IN ONE DIMENSION

Terms related to motion

If you are used to the sport of skating or roller blading, you can see the skater glide along the road often starting at one point and coming to a stop with a twist or a jump at another.

There is a change in the position of the skater from point a to point b. This change of position is defined as displacement. The change in position is measured as the distance from point a to point b travelled and the displacement depends on the velocity that is defined by the skater.

In this lesson, you will learn about displacement, distance, velocity and acceleration and how they are related to each other.

One Dimensional Motion | Representation of One Dimensional Motion | Distance and Displacement | Speed and Velocity

LINEAR MOTION

Graphical representation of linear motion

The graphs of linear motion are used to show displacement at a particular time at a particular velocity. For example, on a displacement-time graph, straight lines indicate constant velocity and curved lines indicate acceleration.

In this lesson, you will learn about displacement-time graphs and acceleration-time graphs.

Displacement Time Graphical Representation

Case 1

Displacement time graph of a stationary object is a straight line parallel to the time axis

Case 2

Displacement time graph of a body moving with uniform velocity is a straight line inclined to the time axis

The velocity can be obtained by finding the slope of the straight line

S ∝ t

Case 3

Displacement time graph of a body moving with variable velocity is a curve

The velocity at any instant can be obtained by finding the slope of the tangent drawn to the curve for that instant of time

EQUATION OF MOTION

Equations of motion

In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of time.  In circumstances of constant acceleration, these simpler equations of motion are usually referred to as the “SUVAT” equations, arising from the definitions of kinematic quantities: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).

First equation of motion – v- u = at.

Second equation of motion – S= ut + 1/2 at2

Third equation of motion – 2as = V2–u2