Nevienmērīga kustība_EN (1)

1. Non-uniform movement

2. Acceleration

Acceleration describes the rapidity of the change in speed. Acceleration is
equal to the change in velocity per unit time.
The "length" of the velocity vector gets longer as the speed increases and shorter as
the speed decreases. As the direction of motion changes, the trajectory of the body
bends - the direction of the velocity vector v changes.

3. Acceleration characteristics

• Like velocity, acceleration is a vector that is directed in the direction of the
instantaneous change in velocity at each instant in time.
• The SI unit of acceleration is metres per second every second (m/s2).
• Suppose we start to observe motion at time t0, when the body is at the origin
x0 and already has an initial velocity v0. Let us also assume that the motion is
in the direction of the x-axis. Since in accelerated motion the velocity
increases by a in each unit of time, the equation for the body's velocity is
• Knowing how the velocity of a body changes, we can derive a coordinate
equation from which we can find the x-coordinate at any instant in time

4.

5. Non-uniform movement graphs 1

The acceleration graph of uniformly accelerated
motion is a straight line parallel to the time axis
because the acceleration does not change.
The speed varies in a steadily accelerating
motion - increasing or decreasing steadily. The
graph of velocity is a straight line with the
equation v = at. The greater the acceleration a ,
the steeper the line.
The path l taken by the body is numerically equal
to the area of the figure bounded by the segment
of the velocity line and the time axis. Since the
shaded figure is a trapezoid, we can use the
formula for calculating the area of a trapezoid

6. Non-uniform movement graphs 2

From coordinate equation
It can be observed, that coordinate dpend motion
time in square. The graph of the path function at
uniform acceleration is a parabola. If the uniformly
accelerated motion is in the same direction, then
the path graph starts from coordinate origin 0 and
the parabola is the same as in the displacement
graph.

7. Free fall and vertical sweep

• When free falling, the body's speed increases uniformly.
• Free fall is a uniformly accelerated movement. If air
resistance is not taken into account, the acceleration is
g=9,8 m/s2.
• Free fall is the movement of a body without initial
velocity and without taking air resistance into account.
• The body can fall vertically in two cases
• it is thrown upwards, reaches its maximum take-off
height h and begins to free fall,
• it is at height h and, having lost its support, falls
vertically downwards.

8. Free fall formulas

• The formula for calculating the uniformly accelerated path is .
Since the motion is in the vertical direction, l = h. Since the initial velocity v0=0,
the equation for the path is
• The velocity at the moment of impact is calculated using the formula v=v0+at.
Since the acceleration is g and the initial velocity is v=v0, v=gt.
• When a body is propelled vertically upwards, the initial velocity of the body is
v0. The height of lift depends on its value. Since the free fall acceleration
vector g is directed opposite to the direction of the initial velocity vector v0,
the motion is uniformly decelerated and the velocity decreases v=v0 - gt .
When the body has reached its maximum height, its velocity becomes zero.
The maximum take-off height h can be determined by

9. Horizontal sweep

In a horizontal sweep, the body is thrown
parallel to the ground, with an initial velocity v0.
The initial velocity vector is directed horizontally
in the direction of motion. A body thrown
horizontally with an initial velocity continues to
move horizontally due to inertia, but is also
attracted to the Earth. The body is therefore
moving along a parabola which is slightly
"flattened" due to air resistance.

10.

The motion of a horizontally ejected body can be
divided into two independent motions. The body
moves uniformly in the horizontal direction with
an initial velocity v0 . At the same time, without
an initial velocity, it is uniformly accelerated
vertically downwards with acceleration g.
In the vertical direction, the motion is free fall, so
the time of fall is given by .
In the horizontal direction the motion is uniform,
so the horizontal distance is calculated
by formula l = v0t .
The instantaneous value of the speed is
calculated according to the formula
vk is the vertical velocity of fall, calculated as
vk=gt .

11. Movement on a circular line

• The numerical value of the speed does not change in a smooth circular
motion.
• The motion of the body along the circular line is periodic - every time T the
body returns to the initial position to start a new orbit. If this motion is
uniform, the time T is called the period of circling or rotation.
• Rotation period - the time during which the body makes one complete
revolution
• The inverse of the period T is called the circular or rotational frequency.
• Rotation frequency - number of revolutions per unit time.
• The period is measured in seconds (s) and the frequency in hertz (Hz). One
hertz means one complete rotation period per second (1 Hz = 1 s-1). Other
units are also used in the technique, such as revolutions per minute (rpm).

12.

When moving about a circular line, the body's
instantaneous velocity vector v is directed along the
tangent of the trajectory. If the motion is uniform, the
modulus of the velocity vector does not change with time.
This velocity is also called the linear velocity. Since the arc
made by the body during the period is equal to the length of
the circular line l=2πR , the linear velocity is equal to
unlike straight-line motion, in circular motion the direction
of the velocity vector changes all the time. Therefore,
motion along a circular line is accelerated motion.
Acceleration is always present and is the cause of the
change in direction of the linear velocity vector.
The centripetal acceleration shows how much and in which
direction the linear velocity changes per unit time. The
centripetal acceleration is perpendicular to the velocity
vector and directed towards the centre of the circular line.

13. Tasks

• In a uniform straight-line motion, the body's velocity changes by 2 m/s per
second. The acceleration of the motion is ...
• A car starts from rest and reaches a speed of 12 m/s in 4 seconds. The
acceleration of the motion is ...
• An elevator car starts moving from rest with an acceleration of 0.3 m/s2. How
much speed will it reach in 2 seconds?
• How does the speed of a cyclist change if the acceleration is negative?
• A motorcycle is moving at 15 m/s. After how many seconds will it stop if the
braking acceleration is 3 m/s2?
• In the first second, the body travels a distance of 8 m, in the second second
again a distance of 8 m, and in the third second again a distance of 8 m. How
much is the acceleration?
• An aeroplane starts moving along a runway with an acceleration of 1.2 m/s2.
How much distance does the aeroplane cover in 10 seconds?

14. Tasks

• The car is travelling at 30 m/s. How many metres is the braking distance of the car
if the braking acceleration is 6 m/s2?
• The equation v=20+2t describes the motion. What is the initial velocity and
acceleration.
• What is the motion of the body if the initial velocity v0 = 10 m/s and the
acceleration a = 1 m/s2 is opposite to the direction of motion!
• What is the equation of the coordinate of the body if the initial coordinate is x0 =
30 m and the velocity is vx = 20 + 2t?
• What is the acceleration of the ball as it rolls along the inclined rim? The ball
travelled 2 metres in 1 second. Assume that the initial velocity of the ball is 0.

15.

• Which graph corresponds to uniformly accelerated motion?

16.

How many metres does the model travel in 14 seconds?

17.

18.

• The free fall time was 8 seconds. From how many metres?
• How many seconds does it take for a stone to fall from a height of 45 metres?
• If a body is thrown vertically upwards at 9.8 m/s, after 1 second its velocity is
... m/s. Ignore air resistance.
• The boys shot a ball vertically upwards and timed the time after which the
ball fell. The ball fell after 4 seconds from the time of firing. What is the
maximum height of the ball if air resistance is ignored?
• The ball starts moving vertically upwards from the ground surface with an
initial velocity of 40 m/s. After how many seconds will it fall back to the
ground? Ignore air resistance.
• If a body is thrown vertically upwards with velocity v, then it will fly to height h.
If a body is thrown with velocity 3v, then it will fly to height...

19.

In a ski jumping competition, the athlete runs before the jump and jumps
from a 5 m high springboard in a horizontal direction at a speed of 5 m/s.
The distance the athlete flies in the horizontal direction is ... m

20.

• Muris the cat jumped out of the window at a horizontal speed of 5 m/s and
reached the ground after 0.7 seconds. At what height was the window?
• A projectile thrown from a height of 20 m in a horizontal direction fell 20 m
from the point of ejection. The velocity of the ball is ... m/s
• A dart is thrown horizontally with an initial velocity of 12 m/s. The dart
reaches the target 32 cm lower than the throwing height. How far is the player
from the target?
• The turbine makes 3000 revolutions per minute. The rotational frequency of
the turbine is ... Hz
• How far along the line of a circle has the cyclist travelled if his displacement
is equal to the diameter of the circle? The radius of the circle is 10 m.
• The circumference of the bicycle wheel is 2 m. The wheel makes one
revolution per second. What is the speed of the bicycle?
• A disc with a radius of 30 cm rotates uniformly on its axis, making 120
revolutions in 1 minute. Determine the linear speed of the outer points of the
disc!
• What is the linear velocity with respect to the centre of the Earth of a
sightseer standing on the Earth's equator, if the radius of the globe is about
6400 km.