MECHANICS

Linear Motion

Non-uniform Linear Acceleration

 theory example#1 example#2

Consider a particle P moving in a straight line from a starting point O.

The displacement from O is x at time t .

The initial conditions are: t ≥ 0 when x=0.

If v is the velocity of P at time t, then :

The acceleration 'a' of particle P is defined as:

or alternately,

Problems on this topic are solved by analysing the information given to form a differential equation. This is then integrated, usually between limits.

Example #1

A particle moves in a straight line such that its acceleration 'a' at time 't' is given by:

If the initial speed of the particle is 5 ms-1, at what values of 't' is the particle stationary?

Example #2

A particle moves from a point O in a straight line with initial velocity 4 ms-1.
if v is the velocity at any instant, the acceleration a of the particle is given by:

The particle passes through a point X with velocity 8 ms-1.

(i) how long does the particle take to reach point X?
(ii) what is the distance OX?(1 d.p.)

(i)

(ii)

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