CEE 102/L
Physics 1 for Engineers
ULO 1b
Kinematics
Metalanguage
Position
The position is the location of the particle from a chosen reference point that we can
consider to be the origin of a coordinate system.
Distance
Distance is the length of a path followed by a particle. It is the total amount of space
that the particle covered during its motion.
Displacement (Δ𝑥)
Displacement of a particle is defined as its change in position in some time interval. It is
a vector quantity and can be either positive or negative and describes how far out of
place the particle is.
Position, Distance and Displacement
The reference point is x=0 and the
car’s initial position is at 30 m to the
right of the origin. Let us define to
the right of the origin as the
positive distance and negative
distance to the left. For every ten
seconds, the car moves from one
point to another. The car moves
back and forth along a straight line
from point A to F.
Speed and Velocity
Speed
Speed, denoted as 𝑣, of an object over a
given time interval is the length of the path it
travels divided by the total elapsed time
Speed and Velocity
Velocity
Velocity denoted as 𝑣̅, during a time interval
Δ𝑡 is the displacement Δ𝑥 divided by Δ𝑡
Acceleration
Acceleration
Acceleration is defined as the change in
velocity over a given time.
Rectilinear Motions
Horizontal motions
Example
The speed of the train is reduced
from 15 m/s to 7 m/s and while
travelling a distance of 90 m.
How much farther will the train
travel before coming to rest,
provided the acceleration
remains constant?
Rectilinear Motions
Vertical motions / Free-falling Bodies
Example
Water drips from the nozzle
of a shower onto the floor
2.45 meter below. How long
will it take for a drop to
reach the floor?
Example 2
A rocket moves straight upward, starting from rest with an
acceleration of +29.4 m/s2. It runs out of fuel at the end of
4.00 s and continues to coast upward, reaching a maximum
height before falling back to Earth. Determine the time for
the rocket to reach the ground and its velocity just before it
hits the ground.
Example 3
A stone is dropped into a well 30 m deep. How long will take
for the sound of the splash be heard? Assume the speed of
sound v = 343 m/s.
Example 4
An car moving at a constant velocity of 15 m/s passes a
gasoline station. Two seconds later, another car leaves the
gasoline station and accelerates at a constant rate of 2
m/s2. How soon will the second car overtake the first?
Seatwork
A ball is thrown from the top of a building with an initial velocity of
20.0 m/s straight upward, at an initial height of 50.0 m above the
ground. The ball just misses the edge of the roof on its way down.
Determine the following:
a. the time needed for the ball to reach its maximum height.
b. the maximum height.
c. the time needed for the ball to return to the height from which it
was thrown and the velocity of the ball at that instant
d. the time needed for the ball to reach the ground
e. the velocity and position of the ball at t = 5.00 s.
Curvilinear Motions
Projectile motions
Curvilinear Motions
Projectile motions
Example 1
An Alaskan rescue plane drops a package of emergency
rations to stranded hikers. The plane is traveling horizontally at
40.0 m/s at a height of 100. m above the ground. Where does
the package strike the ground relative to the point at which it
was released?
Example 2
A long jumper leaves the ground at an angle of 20.0° to the
horizontal and at a speed of 11.0 m/s. How long does it take
for him to reach maximum height? Find the maximum height
it reaches.
Example 3
A projectile is thrown from the top of a building with an
initial velocity of 20 m/s in the horizontal direction. If the
top of the building is 30 m above the ground, how fast will
the projectile be moving just before it hits the ground?
Seatwork
A body is projected upward from the level ground at an
angle of 50° with the horizontal has an initial speed of 40
m/s. How long will it take to hit the ground?