3.6 Motion in a straight line

Ex. 3.5.3.6, 3.7

WOE 3,4,5,6,

Points to Note

**Motion in a straight line**

As the motion is constrained to move on a straight line, choose the straight line in which motion is taking place as X-axis. Hence x represent the position of the particle at any time instant t. If you want you can imagine a graph between t and x but now t in on the vertical axis and x is on the horizontal axis.

Generally origin is taken at the point where the particle is situated at time t = 0.

Position of the particle at time t is given by x and also x measures displacement (not distance).

Velocity is v = dx/dt (3.9)

acceleration is a = dv/dt (3.10)

a = d²x/dt² (3.11)

Decelaration

If acceleration is negative, then it is along the negative X-axis. It is called deceleration

Motion with constant acceleration

Using integration the formulas for v velocity at any instant, x position at any instant and relation between v,u,x and a are derived in this section.

If acceleration is constant dv/dt = a (constant)

initial velocity = u (at time t =0)

final velocity = v (at time t)

Then v = u+at (3.12)

x = distance moved in time t = ut+½at² (3.13)

Also v² = u²+2ax (3.14)

u,v, and a as well as may take negative or positive values. When u, v and a are negative it shows velocity or acceleration is in the negative X direction.

Example 3.5

a) The question asked is distance travelled. The expression for x gives only displacement. But the remark is that as the particle does not turn back it is equal to distance travelled. Be careful when initial velocity is positive and the acceleration is negative.

Example 3.6

There was a past JEE question which is based on the variable defined in the example.

Freely falling bodies

In this case take the Y axis as the straight line on which the particle or body is moving.

You can take height above the ground as +y and work out the problems.

You can take the starting position of the body as the origin and work out the problem.

The choice may be yours or some choice may be more appropriate in case of some problems, be clear of the formula that you have to use depending on the choice you made.

g is approximately equal to 9.8 m/s², but for convenience in many problems it is given as 10m/s².

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