What Is A Negative Velocity

In this commodity, we are going to talk over some negative velocity examples and solve related problems.

Some examples of negative velocity are as follow:-

Object falling downwardly

An object accelerating down from greater heights to down the surface decreases its position while accelerating. Since the position decreases with time, the velocity of the object is negative.

The energy of the object is ever conserved; it only changes from 1 form of energy to another. While the object accelerates upward its kinetic energy utilized for its migrate is converted into potential energy and in one case all the kinetic free energy is converted into the potential free energy, the object starts accelerating down to nothing potential surfaces.

Since the energy is conserved in the class of the potential and kinetic free energy of the object falling from the heights, its initial energy produced will be equal to the final energy.

KE_one+PE_one=KE_ii+PE₂

1/2 mu₁ ²+mgh_ane=1/two mv_two ⁱⁱ+mgh₂

1/2 u_i ²+gh_one=1/2 v_ii ⁱⁱ+gh₂

u₁ ²+2gh₁=v₂ ⁱⁱ+2gh_ii

u₁ ²-five₂ ²=2g(h_ii-h₁)

five₂ ⁱⁱ=u_one ^two-2g(h₂-h_ane)

5_two=√u₁ ⁱⁱ-2g(h₂-h₁)

In short, kinetic energy is equal to the potential energy of the object

i/2 mv²=mgh

five²=2gh

v=√2gh

This implies that the velocity of the object during its flight in the air depends upon the elevation at which it is in a higher place the surface of the footing.

As the pinnacle of the falling object decreases, the velocity of the object will decrease past the foursquare root of its tiptop. Hence the velocity of an object is negative in this instance.

Slipping of feet while trying to climb up the slider

You must have noticed that due to lack of frictional force on the slider, we repeatedly slide backward while climbing upwardly the slider from the slide. This reduces the velocity of a person while climbing and often sliding back to the ground. Hence, this is likewise an example of a negative velocity.

Object slowing down

The fast accelerating object suddenly lowers its velocity and so nosotros have an exponential decrease in the velocity of the object.

negative velocity example — **Graph of an object decreasing its velocity with time**

For such objects, the dispatch will also be negative.

An object moving in a reverse management with high speed

While moving in a reverse direction from the original point and so the position of the object with respect to the origin will decrease, hence the velocity of the object which is a alter in position with time will exist negative.

When the object takes sharp reverse acceleration, so the acceleration is positive but the velocity of the object is negative.

Kingfisher diving in a river for fish

A bird, kingfisher diving into the river water to catch the fish for its food moves with negative velocity as it comes near the surface of the water from the summit at which it was flight.

Light traversing through the medium

As low-cal travels from one medium to another, the speed of calorie-free changes. On entering the denser medium the speed of calorie-free rays decreases, hence is likewise an example of negative velocity, because the distance elapses by the light in the air in one second is more as compared to its velocity in the denser medium, every bit it travels slower comparably.

Read more than on the speed of light.

Spring

Jump e'er tries to regain its original size upon stretching. If a heavy mass is attached to ane terminate of the spring comparable to its leap abiding and keeping the other finish fixed, upon stretching the spring by pulling a mass on a horizontal slide, it will build potential energy which will be converted into kinetic energy once it is released.

The mass will travel in a opposite management due to equal and contrary reactions and will displace at a position towards the stock-still betoken and remain stable. This is an instantaneous procedure. Since the position decreases with fourth dimension the velocity is negative.

Flow of current

The direction of a flow of current is in the direction opposite to the motion of electron charges; this also tin be accounted for a negative velocity of electrons compared to the direction of the electric current.

Solved Problems

Trouble ane: A car travels a distance of 7km in 7min and then slows downwards on reaching the district road and travels 3km in 9minutes. Summate the change in velocity.

Solution: A car displaces seven km from the original point, x₁=7km, time taken t₁=7min;

Hence the speed of the motorcar is

v_i=x₁/t_i=7* 60/7=60km/h

A car travels 3 km in 9 minutes, hence the speed of the auto is

v₂=x_ii/t_ii=iii*60/nine=20km/h

Hence modify in velocity is

Five=5_ii-V_one=xx-60=-40km/h

The change in the velocity of the car becomes negatives one time it slows downwards.

Problem 2: A weight of mass 1kg is kept on a horizontal slide made up of drinking glass. A weight is attached to a leap of length 1 meter whose other finish is sealed in a wall. A mass is pulled to a distance of 50 cm away from its position on applying a strength and relieved. Afterward which the weight displaces 80 cm in a second and rests at a position 80 cm away from the wall.

Discover the instantaneous velocity of a mass and the potential energy of jump on pulling the mass. Also, calculate the potential energy stored in the jump when it was displaced at a distance of 50 cm from its resting position. Given the bound constant k=i.5.

Solution:

Given: 10_ane=50cm, x_ii=80cm, t₁=0, t_two=1sec;

Instantaneous\ Velocity=x_ii-x₁/t₂-t_one=50-80/1-0=-30cm/southward=-0.3m/south

Velocity of a weight is -0.3m/southward which are negative because the weight displaces in the reverse management.

Problem iii: Find the boilerplate velocity of an object traveling with time. The altitude elapsed by the object at different times was noted, the same is shown in the following tabular array. Plot the graph for the same.

Displacement(km)	Time(min)
10	10
viii	20
half-dozen	xxx
iv	40

Solution: The position-time graph for the above information is every bit beneath

Alter in velocity with respect to time is equal to the slope of the graph.

five₁=x₂-x₁/t₂-t_ane=8-x/20-ten=-2/ten=-2*thousand/10*60m/s=-3.3m/s

5₂=10₂-x_ane/t_two-t_ane=6-8/30-xx=-2/10=-two*1000/10* 60m/s=-3.3m/s

v_three=x_ii-10₁/t_two-t₁=iv-half-dozen/40-30=-2/ten=-2*1000/10*60m/southward=-3.3m/s

five₄=x₂-x₁/t₂-t_one=4-viii/twoscore-20=-4/20=-iv*1000/twenty*60m/s=-3.3m/s

It is seen that the velocity of the object remains constant but the position of the object decreases with increasing time, hence the velocity of the object is negative.

The potential energy of a spring is half time the bound constant and a square of the displacement.

U=1/2kx²

=i/2*ane.5*0.five²

=i/2*1.five*0.25

=0.nineteen Joules

Hence, the energy stored in the string was 0.nineteen Joules.

Problem iv: A girl walks 100meters towards Northward in 1minute and returns dorsum to the point from where she had started and walks 200meters towards South from there in 4minutes. Calculate her actual velocity and displacement to accomplish that point where now she is.

Solution: A girl walks 100meters initially towards North in 1minute hence her walking speed was

Speed=Distance/Time

v_i=100/sixty=1.67m/south

Then, a girl covers 200meters in 4minutes, therefore the velocity of a girl is

five_ii=200/four*sixty=0.83m/south

Therefore, the velocity of a girl in 5minutes is

V=V_ii-V_ane=0.83-1.67=-0.84m/south

And actual displacement of a daughter from original position is

x=x₂-ten_i=200-100=100meters

That is 100 meters towards the South from the original position.

Trouble 5: What is the velocity of an object when information technology is at a height of ten meters above the ground and how does the velocity of the object vary at what rate?

Solution: The velocity of the object during its flying in the air is proportional to the foursquare root of its superlative from the ground and the acceleration due to gravity of the World given by the relation

v=√2gh

When the object is at a height of x meters, information technology velocity will be equal to

5=√2*9.eight*10=√196=14 thousand/s

When h=9m

v=√2*9.8*ix=√176.4=13.28 yard/due south

When h=8m

v=√2*nine.8*8=√156.8=12.52 m/southward

When h=7m

v=√2*9.8*vii=√137.2=11.71 m/due south

When h=6m

5=√2*nine.8*six=√117.6=10.84 m/s

When h=5m

v=√two*nine.8*v=√98=9.8 m/southward

When h=4m

v=√2*ix.8*4=√76=8.7 yard/s

When h=3m

v=√2*ix.viii*3=√58.8=7.67 m/s

When h=2m

v=√two*9.8*2=√39.ii=6.26 yard/southward

When h=1m

v=√2*nine.8*i=√19.6=iv.43 m/s

Superlative (m)	Velocity(m/southward)	Acceleration
x	14	-0.72
ix	13.28	-0.76
8	12.52	-0.81
7	11.71	-0.87
six	10.84	-1.04
5	nine.eight	-ane.10
4	8.7	-1.03
3	7.67	-1.41
2	6.26	-one.83
1	4.43	-4.43

This indicates that, as the top decreases, the velocity of an object decreases, and hence dispatch also decreases. The acceleration of the object sharply decreases when information technology is near the ground surface.

Trouble 6: A ray of light enters a saucepan of water and passes through a drinking glass slab placed in it. Find the velocity of the lite rays in each medium. The refractive index of water is i.3 and that of glass is 1.5.

Solution: RI of water is due north=i.3,

due north=c/v

v=c/northward=3⊓*10⁸*ane.3

5=two.3*10⁸m/s

Now the velocity of calorie-free is 2.3*10^viii1000/south. Hence, the speed of light in glass is

northward=v₁/five₂

v₂=five₁/n=two.3*10⁸/1.5

v=1.five*10^eight1000/s

Hence the velocity of lite in glass is *x⁸yard/southward.

Read more on Negative Velocity Graph: Different Graphs And Their Explanations.

Oftentimes Asked Questions

Why velocity is negative?

Velocity is divers as a alter in the position of an object with dissimilar time intervals.

If the position of an object shifts with time, the difference in position with respect to its previous position will exist negative and hence velocity volition be negative compared to the preceding interval.

How stage velocity of light can exist negative?

Distance traveled by a single ray of low-cal or single moving ridge in one 2nd of time is chosen phase velocity.

Negative velocity comes into a scene while light travels from one medium to another because the speed of light decreases on entering the denser medium.