1. RECTILINEAR MOTION OF PARTICLE
◆ Types of Applications:
1. Differentiation Problems:
Given: The relation between the position and the time(x, t).
Required: The velocity v and the acceleration f at any instant.
Method of solution: By differentiation(x, y) we obtain(v, t),
then differentiation(v, t), we obtain(a, t).

2. RECTILINEAR MOTION OF PARTICLE
◆ Types of Applications:
Example:
A particle is moving along a straight line such that its position
is given by:
m, where t is in seconds. Determine the distance
traveled during the first 2 seconds.
Solution:
the distance traveled is determined as follows:

3. RECTILINEAR MOTION OF PARTICLE
◆ Types of Applications:
Solution:
when v = 0:
the solution t=3 sec. is outside the time interval front t=0 to t=2 sec.,
then we determine the position x1 only.

4. RECTILINEAR MOTION OF PARTICLE
◆ Types of Applications:
2. Integration Problems:
Given: The acceleration(a, t) and the initial conditions x0, v0.
Required: The position (x, t).
Method of solution:
substitute a = dv/dt in the relation(a, t), the first integration
step results in (v, t), v = dx/dt in the relation (v, t) and integrate
again, the relation (x, t) will be obtained.

5. RECTILINEAR MOTION OF PARTICLE
◆ Types of Applications:
Example:
A particle is moving along a straight line such that its acceleration
is given by:
, where t is in seconds. If the motion is started
from the origin with a velocity of 5m/sec., determine the distance
it travels during the first 6 seconds.
Solution:

6. RECTILINEAR MOTION OF PARTICLE
◆ Types of Applications:
Solution:
when v = 0: