## [Tổng Hợp] all the formulas for calculating instantaneous velocity Complete & accurate

Instantaneous velocity vectors are an important concept in physics from middle school to high school. Together with Le Hong Phong High School review all the formulas for calculating instantaneous velocity vectors Full & accurate from the general instantaneous velocity vector calculation formula, the average instantaneous velocity vector calculation formula and the Instantaneous velocity vector calculation in particular!

## Some formulas for calculating instantaneous velocity vectors

### What is instantaneous velocity vector?

It is important to first understand the concept of instantaneous velocity vectors. According to Wikipedia an instantaneous velocity vector is a physical quantity that describes the degree of travel in different states such as speed or direction of travel, determined by the ratio of the displacement of an object at a particular time interval. body. The instantaneous velocity vector will be represented by the vector.

### Formula for calculating instantaneous velocity

It is necessary to understand the basic instantaneous velocity vector calculation formula that is:In there:

- s: length of travel distance.
- t: time required to complete the journey.
- v: speed of travel.

For example:

Lesson 1: On the same distance of 24 km, the car takes the remaining 24 minutes and the motorbike takes 36 minutes. Which car’s instantaneous velocity vector is greater and by how many km/h?

Solution: Change 24 minutes = 0.4 hours

36 minutes = 0.6 hours

The instantaneous velocity of the car is:

24 : 0.4 = 60 (km/hr)

The instantaneous velocity of the motorcycle is:

24 : 0.6 = 40 (km/h)

The instantaneous velocity vector of the car is larger than the instantaneous velocity of the motorcycle and greater than that:

60 – 40 = 20 (km/hr)

Answer: 20 km/h

Exercise 2: Distance AB is 135 km long. The car goes from A to B in 2 hours 30 minutes. Calculate the instantaneous velocity of the car, given that the car rests for 15 minutes along the way.

Prize:

The time taken by the car to travel distance AB (excluding rest time) is:

2 hours 30 minutes – 15 minutes = 2 hours 15 minutes

2 hours 15 minutes = 2.25 hours

The instantaneous velocity of the car is:

135 : 2.25 = 60 (km/h)

Answer: 60km/h

### The formula for calculating the average instantaneous velocity

What is the average instantaneous velocity vector? The instantaneous velocity vector has a change with time then we will have the average instantaneous velocity vector. The average instantaneous velocity vector is the ratio between the change of position for the time period under consideration and that time interval.

The formula for calculating average instantaneous velocity:

In there:

- : average instantaneous velocity vector
- s: distance traveled.
- t: time required to travel the entire distance s
- : time to go all the way s1;s2; s3
- v1, v2, v3: instantaneous velocity vector transported over distance s1, s2, s3

For example:

Exercise 1: A car travels from A to B. In the first 3/4 of the distance, the car travels with an instantaneous velocity of 36km/h. The remaining distance traveled by the car in 10 minutes with an instantaneous velocity of 24km/h. Calculate the average instantaneous velocity of the car over the whole distance AB.

Prize:

The length of the following distance is S2 = t2.v2 = 24. 1/6 = 4km.

The length of the first distance is S1 = 3S2 = 12km.

The total length of the distance AB is S = S1 + S2 = 12 + 4 = 16km.

Time to complete the first distance is t1 = 12/36 = 1/3 (h)

Total time to cover the distance AB is t = t1 + t2 = 1/3 + 1/6 = 1/2 (h)

the average instantaneous velocity vector is v = S/t = 16/(1/2) = 32km/h

Exercise 2: A car travels from A to B. The first half time the instantaneous velocity vector of the car is v1 = 60km/h, the second half time the instantaneous velocity vector of the car is v2 = 40km/h. Calculate the average instantaneous velocity of the car over the whole distance AB.

Prize

Let t be the total time it takes the car to travel from A to B, and v is the average instantaneous velocity of the car.

The length of the distance AB is: S = vt (1)

According to the article we have:

From (1) and (2) vt = 50t → → v = 50km/h

### Formula for calculating instantaneous velocity vector

what is instantaneous velocity vector in physics 10? Instantaneous velocity vector can be understood as the speed, slowness and direction of travel at a specific time on the object’s transport distance.

If you want to calculate the instantaneous instantaneous velocity vector at a specific moment, you need to consider the average instantaneous velocity vector at an infinitesimal time interval from that moment:

The formula for calculating instantaneous velocity vector:

- v is the instantaneous velocity vector.
- r is a position vector similar to a function of time.
- t is the time.

For example:

Lesson 1. After starting 5s, the instantaneous velocity vector of a rocket is 360km/h. Consider the rocket to accelerate steadily.a/ Make a formula to calculate the instantaneous velocity vector of the rocket?b/ Calculate the instantaneous velocity vector of the rocket after 10 s of departure?

Prize:

a/ + option: * Positive direction in the same direction of travel .* The origin of time is the moment the rocket starts: t0 = 0.+ Find acceleration a: Yes: v1 = 0; v2 = 360km/h = 100m/s ; Δt= 5s.→ a = ΔV/Δt=(100−0):5= 20m/s2.+ At t0 = 0, then v0 = 0.+ So: v = v0 + a.(t – t0) = 0 + 20 (t – 0) = 20t (m/s)*Note: if the positive direction is selected in the opposite direction of travel, then: v = -20t (m/s).b/ instantaneous velocity vector of the rocket after starting 10s: has t = 10s → v = 20t = 20. 10 = 200m/s = 720km/h.

Lesson 2. An object moving in a straight line changes uniformly with an initial instantaneous velocity vector of v0 = -10m/s and an acceleration a = 0.5m/s2.a/Formulating the instantaneous velocity vector formula time?b/How long will it take for the object to stop?

Prize:

a/+ choose the time origin as the first instant.+ We have v = v0 +at = -10 + 0.5t.*Remarks: This topic has mentioned both the sign of the instantaneous velocity and acceleration should not be positive.b/ Time from first moment to stop: v = -10 + 0.5t = 0 → t = 20(s)

### Addition of instantaneous velocity vectors in mechanics

For the purpose of converting instantaneous velocity vectors to different frames of reference, we need to use the addition of instantaneous velocity vectors in classical mechanics. Instantaneous velocity vector addition is simply understood as ordinary vector addition.

In there:

- vAB instantaneous velocity vector A with B
- vAC instantaneous velocity vector A with C
- vCB instantaneous velocity vector C with B

### Simple instantaneous velocity vector exercise

Exercise 1: Take a bicycle to travel a distance from A to B. In the first 3/4 of the distance, the bike travels with an instantaneous velocity vector v1. The remaining distance traveled by the car in a period of 10 minutes with an instantaneous velocity vector v2 = 24km/h. Given the average instantaneous speed of the car, the distance AB is v = 32km/h. Students calculate v1.

Hints for problem 1:

The length of the following distance: S2 = t2. v2 = 24. 1/6 = 4km.

First distance: S1 = 3S2 = 12km.

Total length of distance AB: S = S1 + S2 = 12 + 4 = 16km.

First distance transport time: t = S/v = 16/32 = 0.5h

First distance transport time t1 = t – t2 = 0.5 – 1/6 = 1/3 (h)

instantaneous speed vector of the bicycle at first distance v1 = S1/t1 = 12/(1/3) = 36km/h

Exercise 2: There is a car traveling from A to B. In the first half of the segment the instantaneous velocity vector is v1, the remaining distance the instantaneous velocity vector of the car is v2. Find the average instantaneous velocity vector over the entire journey.

Hints for problem 2:

We call S the length of the distance AB, and v the vector of the average instantaneous velocity of the distance AB.

The time taken by the car to travel from A to B is t = S/v (1)

Lesson 3: A car transports from A to B. The length of A to B is 63km. The first time the car transports 63km/h, then the car moves erratically at 54km/h at 45km/h… when it reaches B, the car is only 10km/h. Shipping time is 1 hour 45 minutes. Calculate the average instantaneous velocity vector traveled over the distance AB.

Hints for problem 3:

Transport time to the end of the distance AB with t=1h45′ = 1.75h. S=45km.

The average instantaneous velocity of the vehicle traveling on the road segment AB will be

=> The average instantaneous speed vector of the car traveling the whole distance AB is 36km/h.

Lesson 4. A moving body changes uniformly with an initial instantaneous velocity vector of v0 = -20m/s and an acceleration a = -2m/s2. Calculate the object’s instantaneous velocity vector 10s later?

Hints for problem 4:

+ choose the time origin as the first instant.+ Yes v = v0 + at = -20 -2t → the instantaneous velocity vector at t = 10s is: v = -20 – 2. 10 = -40m/s. * Comment: This object moves faster and faster in the negative direction.

Lesson 5. A motorcycle is traveling straight ahead with an instantaneous velocity of 54km/h when the brakes are applied and it slows down steadily. After braking for 4s, the tachometer is only 18km/ha/ Formulate the instantaneous instantaneous velocity vector of the machine since braking?b/ How long does it take to stop the car after braking?

Suggestions for solving lesson 5:

a/ + option: * Positive direction goes in the same direction.* The origin of time is the moment when the motorcycle starts to brake: t0 = 0.+ Find acceleration a: Yes: v1 = 54km/h = 15m/s; v2 = 18km/h = 5m/s ; t = 4s.→ a = V2−V1/Δt=5−15/4 = -2.5 m/s2.+ At t0 = 0, v0 = 15m/s.+ So v = v0 + at = 15 – 2 ,5t (m/s)*Note: if the positive direction is selected in the opposite direction, then: v = -15 + 2.5.t (m/s).b/ At stop the instantaneous velocity vector instantaneous speed of the car v = 0. so the time it takes for the car to stop from the moment the brake is applied: v = 15 – 2.5t = 0 → t = 15/ 2.5 = 6(s).

Exercise 6. A ball rolls uniformly slowly up a slope with an initial instantaneous velocity vector at the bottom of the slope of 20 m/s. After stopping at the top of the slope, it rolled back along the old road quickly and steadily. Knowing when rolling up as well as rolling down its acceleration vectors are both directed parallel to the slope from the top down and have a constant magnitude of 2m/s2.a/ Make a formula for the instantaneous velocity vector of the ball during rolling up and down? b/ How long does it take for the ball to stop at the top of the slope from the bottom of the slope? c/ 14 seconds after rolling off the bottom of the slope, what is the speed of the ball? Which direction is it going at that time? Hints to solve problem 6:

a/ + options: * Positive direction is in the same direction as the ball rolls up.* The origin of time is the moment when the ball is at the bottom of the slope.+ Since the opposite direction is positive, its algebraic value a = -2m/s2 .+ At t0 = 0, v0 = 20m/s.(Because

V0−→

direction in the positive direction).+ So v = v0 + at = 20 – 2.t (m/s)b/ At stopping the ball’s instantaneous velocity vector is zero.so the moment the ball stops: v = 20 – 2.t = 0 → t = 10(s)So after rolling off the foothill 10s the ball stops.c/ instantaneous velocity vector of the ball at t = 14s:v = 20 – 2.t = 20 – 2.14 = 20 – 28 = -8(m/s)v = – 8m/s

Lesson 7: A person rides a motorbike on a distance, in the first 1.5 hours he travels with an instantaneous speed of 48 km/h, in 0.5 hours he travels with an instantaneous speed of 40. km/hr. What is the average instantaneous velocity vector of that person over the entire distance traveled?

Suggestions for solving problem 7:

The distance traveled by the person in the first 1.5 hours is:

48 x 1.5 = 72 (km)

The distance traveled by the person in the following 0.5 hours is:

40 x 0.5 = 20 (km)

The total distance traveled by the person is:

72 + 20 = 92 (km)

The time the person has gone is:

1.5 + 0.5 = 2 (hours)

The vector of the average instantaneous velocity of that person is:

92 : 2 = 46 (km/h)

A/S. 46 km/h

similarly we have just mentioned the formulas for calculating instantaneous velocity vectors such as the formula for calculating the average instantaneous velocity vector, the formula for calculating the instantaneous velocity vector, the addition of the instantaneous velocity vector and the some exercises on simple instantaneous velocity vectors. Hope the above knowledge will help you to solve all kinds of problems in class as well as review with good results. Remember to see more formulas for calculating distance.

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