POSITION, VELOCITY, AND
ACCELERATION
Review- 3-C
Position:
x(t)
Velocity: v(t)  x (t)
Acceleration: a(t)  v (t)  x (t)


dx

speed

v
(
t
)

x
(t ) 

dt
b

disp :  v(t )dt
a
Acceleration vs Velocity
• If the signs are the same, then the particle’s
speed is increasing
• If the signs are opposite, then the particle’s
speed is decreasing
• If the velocity is zero and acceleration is not
zero, then the particle is momentarily
stopped and changing directions.
Velocity
• If v(t) > 0 then the particle is moving to the
right
• If v(t) < 0 then the particle is moving to the
left
• If v(t) = 0 then the particle has momentarily
stopped or is changing directions
1) The position of a particle moving along the
x - axis at time t is given by
3
2
x(t )  4t  42t  120t  95 for 0≤ t ≤ 20
a) Determine when the particle is moving to the left?
1) The position of a particle moving along the
x - axis at time t is given by
3
2
x(t )  4t  42t  120t  95 for 0≤ t ≤ 20
b) Determine when the particle changes direction and
find its position.
1) The position of a particle moving along the
x - axis at time t is given by
3
2
x(t )  4t  42t  120t  95 for 0≤ t ≤ 20
c) Determine when the particle is speeding up?
1) The position of a particle moving along the
x - axis at time t is given by
3
2
x(t )  4t  42t  120t  95 for 0≤ t ≤ 20
d) find the total distance travelled
2) An object is moving along the x-axis
1
according to x(t )  t 3  8t 2  18t  10
3
for t ≥ 0 find all intervals during which
the object is moving in a positive direction.
3) An object is moving along the x-axis
 t 
according to x(t )  sin  
3
for 0≤ t ≤ 6 find the intervals during which
the object is speeding up.
4
2
x
(
t
)

t

8
t
4) If
a) find the total distance traveled by the
particle on the interval (0,4).
b) Find the displacement on the interval (0,4).
HOME WORK
Assignment 3-C
position, velocity and
acceleration.