Sign Convention for Displacement

Displacement is a vector quantity, i.e., it has both magnitude and direction.
While dealing with a one-dimensional motion, it will have only two directions.

Example-

Up or Down
Right or Left
North or South
East or West

In a one-dimensional motion, generally positive and negative signs are assigned to the two possible directions.

Note

Here, negative doesn't mean being inferior. It is just to indicate that if we have assigned one direction as positive then, other is negative.
Also, assigning the sign to direction is random (i.e., completely on one's choice).

Thus, in a one-dimensional analysis, vector quantity can be fully expressed by assigning positive and negative signs.

Steps to determine the sign of displacement

Step 1

Identify origin. Generally, a starting point is taken as the origin.

Step 2

Assign one direction as positive and other as negative or as given in the question.

Step 3

Draw a figure corresponding to the time when the sign of displacement is to be determined.

(a) If the particle is on the positive side of origin then displacement is positive.

(b) If the particle is on the negative side of origin then displacement is negative.

Note

While determining the sign of displacement disregard the direction in which the body is moving.

Illustration Questions

A particle is moving along a straight line. It starts from A (origin) and goes to C through B and then returns to E through D. Comment on the sign of displacement at B, C, D and E.

A Displacement at B and C are negative and at D and E are positive

B Displacement at B ,C and D are negative and at E is positive

C Displacement at B ,C and D are positive and at E is negative

D Displacement at B , C and E are positive and at D is negative

B, C, and D are on the positive side of origin so, displacements at B, C and D are positive.

E is on negative side of origin, so displacement at E is negative.

A particle is moving along a straight line. It starts from A (origin) and goes to C through B and then returns to E through D. Comment on the sign of displacement at B, C, D and E.

Displacement at B and C are negative and at D and E are positive

Displacement at B ,C and D are negative and at E is positive

Displacement at B ,C and D are positive and at E is negative

Displacement at B , C and E are positive and at D is negative

Option C is Correct

Sign Convention for Velocity

For a one-dimensional motion, identify origin (generally starting point) and assign one side as positive and other as negative.
A particle moving in the positive direction has positive velocity and if moving in the negative direction, then has a negative velocity.

Note: Disregard the location. Just observe the direction in which the particle is moving. If it is moving in the positive direction then positive velocity and if it is moving in the negative direction, then negative velocity.

Steps to check direction of motion at the point

If a particle is moving in the negative direction, velocity is negative.
If a particle is moving in the positive direction, velocity is positive.

Illustration Questions

A particle, in one dimensional motion, starts moving from A to C through B and returns to E through D. Comment on the sign of velocity at B and D.

A Velocity is negative at B and positive at D

B Velocity is positive at B and negative at D

C Velocity is positive at both B and D

D Velocity is negative at both B and D

At B, the particle is moving in positive direction, so its velocity at B is positive.

At D, the particle is on the positive side of origin but it is moving towards negative direction, so velocity at D is negative.

Hence, option B is correct.

A particle, in one dimensional motion, starts moving from A to C through B and returns to E through D. Comment on the sign of velocity at B and D.

Velocity is negative at B and positive at D

Velocity is positive at B and negative at D

Velocity is positive at both B and D

Velocity is negative at both B and D

Option B is Correct

Illustration Questions

A particle is moving from A to C through B with a decreasing speed. Comment on the sign of velocity and acceleration at B.

A Velocity is positive, acceleration is negative

B Velocity is negative, acceleration is positive

C Velocity is positive, acceleration is positive

D Velocity is negative, acceleration is negative

Sign of velocity

At B, particle is moving towards C, i.e., in positive direction.

Therefore, velocity is positive at B.

Sign of acceleration

Since, velocity is positive and speed is decreasing, therefore, acceleration is negative at B.

A particle is moving from A to C through B with a decreasing speed. Comment on the sign of velocity and acceleration at B.

Velocity is positive, acceleration is negative

Velocity is negative, acceleration is positive

Velocity is positive, acceleration is positive

Velocity is negative, acceleration is negative

Option A is Correct

Illustration Questions

A particle is moving from C to A through B with a uniform speed. Comment on the sign of displacement and velocity at B.

A Displacement is positive, velocity is negative

B Displacement is negative, velocity is positive

C Displacement is positive, velocity is positive

D Displacement is negative, velocity is negative

Assuming A as origin.

Sign of displacement

Since, B is on positive side of origin so, displacement at B is positive.

Sign of velocity

At B, particle is moving towards A, i.e., in negative direction, therefore, velocity at B is negative.

A particle is moving from C to A through B with a uniform speed. Comment on the sign of displacement and velocity at B.

Displacement is positive, velocity is negative

Displacement is negative, velocity is positive

Displacement is positive, velocity is positive

Displacement is negative, velocity is negative

Option A is Correct

Sign Convention for Acceleration

Acceleration has the same sign as that of force.
If the force acting on a particle is in the direction of its velocity, its speed increases.
If the force acting on a particle is opposite to the direction of velocity, its speed decreases.

Sign of acceleration

1. If velocity is positive and its magnitude is increasing, then acceleration is positive.

2. If velocity is positive and its magnitude is decreasing, then acceleration is negative.

3. If velocity is negative and its magnitude is increasing, then acceleration is negative.

4. If velocity is negative and its magnitude is decreasing, then acceleration is positive.

Illustration Questions

A particle is moving in positive direction with decreasing speed, determine the sign of acceleration.

A Positive

B Negative

C Can't be determined

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$url = 'https://www.actucation.com/'
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$j = (int) 2
$str = '<h2><strong>Sign of acceleration</strong></h2>

<p>1. If&nbsp;velocity&nbsp;is positive and its magnitude is increasing, then acceleration is positive.</p>

<p>2.&nbsp;If&nbsp;velocity&nbsp;is&nbsp;positive&nbsp;and its magnitude is decreasing, then acceleration is negative.</p>

<p>3.&nbsp;If velocity is negative and its magnitude is increasing, then acceleration is negative.</p>

<p>4.&nbsp;If&nbsp;velocity&nbsp;is negative and its magnitude is decreasing, then acceleration is positive.</p>
'
$pos = false
$pos2 = false
$header = ''
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include - APP/View/Elements/theorypage.ctp, line 161
View::_evaluate() - CORE/Cake/View/View.php, line 935
View::_render() - CORE/Cake/View/View.php, line 897
View::_renderElement() - CORE/Cake/View/View.php, line 1195
View::element() - CORE/Cake/View/View.php, line 412
include - APP/View/Students/subject.ctp, line 10
View::_evaluate() - CORE/Cake/View/View.php, line 935
View::_render() - CORE/Cake/View/View.php, line 897
View::render() - CORE/Cake/View/View.php, line 466
Controller::render() - CORE/Cake/Controller/Controller.php, line 952
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160
[main] - APP/webroot/index.php, line 122

Notice (8): Undefined offset: 3 [APP/View/Elements/theorypage.ctp, line 165]Code Context                                    

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$str = '<h2><strong>Sign of acceleration</strong></h2>

<p>1. If&nbsp;velocity&nbsp;is positive and its magnitude is increasing, then acceleration is positive.</p>

<p>2.&nbsp;If&nbsp;velocity&nbsp;is&nbsp;positive&nbsp;and its magnitude is decreasing, then acceleration is negative.</p>

<p>3.&nbsp;If velocity is negative and its magnitude is increasing, then acceleration is negative.</p>

<p>4.&nbsp;If&nbsp;velocity&nbsp;is negative and its magnitude is decreasing, then acceleration is positive.</p>
'
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include - APP/View/Elements/theorypage.ctp, line 165
View::_evaluate() - CORE/Cake/View/View.php, line 935
View::_render() - CORE/Cake/View/View.php, line 897
View::_renderElement() - CORE/Cake/View/View.php, line 1195
View::element() - CORE/Cake/View/View.php, line 412
include - APP/View/Students/subject.ctp, line 10
View::_evaluate() - CORE/Cake/View/View.php, line 935
View::_render() - CORE/Cake/View/View.php, line 897
View::render() - CORE/Cake/View/View.php, line 466
Controller::render() - CORE/Cake/Controller/Controller.php, line 952
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160
[main] - APP/webroot/index.php, line 122

Since, particle is moving in positive direction so, velocity is positive.

Since, velocity is positive and speed is decreasing, therefore, acceleration is negative.

A particle is moving in positive direction with decreasing speed, determine the sign of acceleration.

Positive

Negative

Can't be determined

Notice (8): Undefined offset: 3 [APP/View/Elements/theorypage.ctp, line 285]

Code Context

                                            ?>

                                        </div>

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$str = '<h2><strong>Sign of acceleration</strong></h2>

<p>1. If&nbsp;velocity&nbsp;is positive and its magnitude is increasing, then acceleration is positive.</p>

<p>2.&nbsp;If&nbsp;velocity&nbsp;is&nbsp;positive&nbsp;and its magnitude is decreasing, then acceleration is negative.</p>

<p>3.&nbsp;If velocity is negative and its magnitude is increasing, then acceleration is negative.</p>

<p>4.&nbsp;If&nbsp;velocity&nbsp;is negative and its magnitude is decreasing, then acceleration is positive.</p>
'
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include - APP/View/Elements/theorypage.ctp, line 285
View::_evaluate() - CORE/Cake/View/View.php, line 935
View::_render() - CORE/Cake/View/View.php, line 897
View::_renderElement() - CORE/Cake/View/View.php, line 1195
View::element() - CORE/Cake/View/View.php, line 412
include - APP/View/Students/subject.ctp, line 10
View::_evaluate() - CORE/Cake/View/View.php, line 935
View::_render() - CORE/Cake/View/View.php, line 897
View::render() - CORE/Cake/View/View.php, line 466
Controller::render() - CORE/Cake/Controller/Controller.php, line 952
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160
[main] - APP/webroot/index.php, line 122

"> D

Notice (8): Undefined offset: 3 [APP/View/Elements/theorypage.ctp, line 289]Code Context                                            

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$url = 'https://www.actucation.com/'
$i = (int) 4
$j = (int) 2
$str = '<h2><strong>Sign of acceleration</strong></h2>

<p>1. If&nbsp;velocity&nbsp;is positive and its magnitude is increasing, then acceleration is positive.</p>

<p>2.&nbsp;If&nbsp;velocity&nbsp;is&nbsp;positive&nbsp;and its magnitude is decreasing, then acceleration is negative.</p>

<p>3.&nbsp;If velocity is negative and its magnitude is increasing, then acceleration is negative.</p>

<p>4.&nbsp;If&nbsp;velocity&nbsp;is negative and its magnitude is decreasing, then acceleration is positive.</p>
'
$pos = false
$pos2 = false
$header = ''
$m = (int) 2
$correctOption = 'B'
include - APP/View/Elements/theorypage.ctp, line 289
View::_evaluate() - CORE/Cake/View/View.php, line 935
View::_render() - CORE/Cake/View/View.php, line 897
View::_renderElement() - CORE/Cake/View/View.php, line 1195
View::element() - CORE/Cake/View/View.php, line 412
include - APP/View/Students/subject.ctp, line 10
View::_evaluate() - CORE/Cake/View/View.php, line 935
View::_render() - CORE/Cake/View/View.php, line 897
View::render() - CORE/Cake/View/View.php, line 466
Controller::render() - CORE/Cake/Controller/Controller.php, line 952
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160
[main] - APP/webroot/index.php, line 122

Notice (8): Undefined offset: 3 [APP/View/Elements/theorypage.ctp, line 296]Code Context                                            <?php 

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$url = 'https://www.actucation.com/'
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$str = '<h2><strong>Sign of acceleration</strong></h2>

<p>1. If&nbsp;velocity&nbsp;is positive and its magnitude is increasing, then acceleration is positive.</p>

<p>2.&nbsp;If&nbsp;velocity&nbsp;is&nbsp;positive&nbsp;and its magnitude is decreasing, then acceleration is negative.</p>

<p>3.&nbsp;If velocity is negative and its magnitude is increasing, then acceleration is negative.</p>

<p>4.&nbsp;If&nbsp;velocity&nbsp;is negative and its magnitude is decreasing, then acceleration is positive.</p>
'
$pos = false
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$header = ''
$m = (int) 2
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include - APP/View/Elements/theorypage.ctp, line 296
View::_evaluate() - CORE/Cake/View/View.php, line 935
View::_render() - CORE/Cake/View/View.php, line 897
View::_renderElement() - CORE/Cake/View/View.php, line 1195
View::element() - CORE/Cake/View/View.php, line 412
include - APP/View/Students/subject.ctp, line 10
View::_evaluate() - CORE/Cake/View/View.php, line 935
View::_render() - CORE/Cake/View/View.php, line 897
View::render() - CORE/Cake/View/View.php, line 466
Controller::render() - CORE/Cake/Controller/Controller.php, line 952
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 192
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 160
[main] - APP/webroot/index.php, line 122

Option B is Correct

Sign Convention for Analyzing Free Fall Motion

The direction of the acceleration due to gravity (g), is always towards the center of earth.
The same is true for the direction of force of gravity.
If we assume downward direction to be positive, then acceleration due to gravity and force of gravity are positive.
Similarly, if we assume downward direction to be negative, then acceleration due to gravity and force of gravity are negative.
'g' is also called free-fall acceleration.

Illustration Questions

A particle is thrown vertically upward. What will be the sign of direction of acceleration due to gravity in upward motion, if downward direction is taken positive?

A Positive

B Negative

C Zero

D None of these

The direction of the acceleration due to gravity is always towards the center of earth.

Since, downward direction is taken positive.

Thus, acceleration due to gravity is positive in downward direction.

Hence, in upward motion, the acceleration due to gravity is negative.

A particle is thrown vertically upward. What will be the sign of direction of acceleration due to gravity in upward motion, if downward direction is taken positive?

Positive

Negative

Zero

None of these

Option B is Correct