Uniform motion

Speed, average speed, coordinate versus time, graphs of velocity, displacement, distance and coordinate.

Terms

Studied 0 of 5

Formulas

Speed of uniform motion

v = \dfrac{s}{t}

Quantities
Symbol	Name	Unit
$v$	speed	m/s
$s$	distance	m
$t$	time	s

Solved for another quantity:

s = v\,t

t = \dfrac{s}{v}

Note. Watch the units: distance in km and time in hours give speed in km/h.

Average speed

v_{\text{ср}} = \dfrac{s_1 + s_2 + \dots}{t_1 + t_2 + \dots}

Quantities
Symbol	Name	Unit
$v_{\text{ср}}$	average speed	m/s
$s_1, s_2$	distances of the parts	m
$t_1, t_2$	times of the parts	s

Note. The first half of the way at 40 km/h, the second half at 60 km/h. The average speed is 48 km/h, not 50.

Coordinate in uniform motion

x = x_0 + v_x\,t

Quantities
Symbol	Name	Unit
$x$	coordinate at time $t$	m
$x_0$	initial coordinate	m
$v_x$	velocity component	m/s
$t$	time	s

Solved for another quantity:

v_x = \dfrac{x - x_0}{t}

t = \dfrac{x - x_0}{v_x}

Note. If the body moves against the axis, substitute $v_x$ with a minus sign.

Displacement component

s_x = v_x\,t

Quantities
Symbol	Name	Unit
$s_x$	displacement component	m
$v_x$	velocity component	m/s
$t$	time	s

Solved for another quantity:

x = x_0 + s_x

Lab

Set the quantities with the sliders. The graphs and the formulas with your numbers update at once.

Motion of the body

Drag the cart with the mouse to set its starting position. The dots mark the body's position every 1 s.

t

= 0 sPlayback speed

Graphs

The graphs are drawn as the body moves. Click a graph to move through the recording.

x(t)

s_x(t)

$s_x = x - x_0$ . It decreases when the body moves against the axis.

l(t)

Distance never decreases: after a turnaround it grows while $s_x$ shrinks.

v_x(t)

The shaded area is the displacement $s_x$ .

t

0 s

s_x

0 m

l

0 m

Formulas with your numbers

x = x_0 + v_x t = -15 + 3\cdot 0 = -15\ \text{m}

Lab «Moving man»

Drag the man by hand — the x(t), v(t) and a(t) graphs draw themselves. Then set the motion with numbers or repeat a graph.

Open full screen →

How to read the graphs

$x(t)$ is a straight line. The steeper it is, the greater the speed. If it goes down, $v_x < 0$ .
$v_x(t)$ is a horizontal line: the velocity is constant. The area under it up to time $t$ equals the displacement $s_x$ .
Distance $l(t)$ never decreases, while displacement $s_x(t)$ decreases when $v_x < 0$ .
Rest is a horizontal line on the $x(t)$ graph and zero on the $v_x(t)$ graph.

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Terms

Studied 0 of 5

Formulas

Speed of uniform motion

v = \dfrac{s}{t}

Quantities
Symbol	Name	Unit
$v$	speed	m/s
$s$	distance	m
$t$	time	s

Solved for another quantity:

s = v\,t

t = \dfrac{s}{v}

Note. Watch the units: distance in km and time in hours give speed in km/h.

Average speed

v_{\text{ср}} = \dfrac{s_1 + s_2 + \dots}{t_1 + t_2 + \dots}

Quantities
Symbol	Name	Unit
$v_{\text{ср}}$	average speed	m/s
$s_1, s_2$	distances of the parts	m
$t_1, t_2$	times of the parts	s

Note. The first half of the way at 40 km/h, the second half at 60 km/h. The average speed is 48 km/h, not 50.

Coordinate in uniform motion

x = x_0 + v_x\,t

Quantities
Symbol	Name	Unit
$x$	coordinate at time $t$	m
$x_0$	initial coordinate	m
$v_x$	velocity component	m/s
$t$	time	s

Solved for another quantity:

v_x = \dfrac{x - x_0}{t}

t = \dfrac{x - x_0}{v_x}

Note. If the body moves against the axis, substitute $v_x$ with a minus sign.

Displacement component

s_x = v_x\,t

Quantities
Symbol	Name	Unit
$s_x$	displacement component	m
$v_x$	velocity component	m/s
$t$	time	s

Solved for another quantity:

x = x_0 + s_x

Lab

Set the quantities with the sliders. The graphs and the formulas with your numbers update at once.

Motion of the body

Drag the cart with the mouse to set its starting position. The dots mark the body's position every 1 s.

t

= 0 sPlayback speed

Graphs

The graphs are drawn as the body moves. Click a graph to move through the recording.

x(t)

s_x(t)

$s_x = x - x_0$ . It decreases when the body moves against the axis.

l(t)

Distance never decreases: after a turnaround it grows while $s_x$ shrinks.

v_x(t)

The shaded area is the displacement $s_x$ .

t

0 s

s_x

0 m

l

0 m

Formulas with your numbers

x = x_0 + v_x t = -15 + 3\cdot 0 = -15\ \text{m}

How to read the graphs

x(t)

is a straight line. The steeper it is, the greater the speed. If it goes down,

v_x < 0

v_x(t)

is a horizontal line: the velocity is constant. The area under it up to time

t

equals the displacement

s_x

Distance

l(t)

never decreases, while displacement

s_x(t)

decreases when

v_x < 0

Rest is a horizontal line on the

x(t)

graph and zero on the

v_x(t)

graph.