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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 :

 

v equals dx by dt

 

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

 

definition of acceleration in terms of v and x

 

or alternately,

 

non uniform acceleration differential equations

 

 

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

 

 

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Example #1

 

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

 

problem #01a

 

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

 

 

problem #01b

 

 

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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:

 

problem 2a

 

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)

problem #2b

 

 

(ii)

problem 2c

 

 

 

 

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