# Instanteneous velocity question

• jhson114
In summary, The speed of car A needs to be greater than car B in order for it to pass car B while traveling at constant velocity. If car B is accelerating, car A must still have a greater velocity at the time of passing in order to successfully pass car B.)
jhson114
two cars A and B are traveling in a straight line. Car A is passing car B and at time t1, car A is adjacent to car B. If each cars are traveling in a constant speed ( each with separate constant speed), at time t1, instanteneous velocity of car A should be greater than car B right?? since in order for car A to pass car B, velocity of car A has to be greater than car B, and since their velocity is constant throughout motion, car A should have greater instanteneous velocity at t1.
also, it shouldn't matter if car B is accelerating and car A is traveling in a constant velocity.. right? since even though B is accelerating car A must have greater velocity at t1 in order to pass car B, therefore instanteneous of car A should still be greater. please correct me if I'm wrong. thank you

jhson114 said:
two cars A and B are traveling in a straight line. Car A is passing car B and at time t1, car A is adjacent to car B. If each cars are traveling in a constant speed ( each with separate constant speed), at time t1, instanteneous velocity of car A should be greater than car B right?? since in order for car A to pass car B, velocity of car A has to be greater than car B, and since their velocity is constant throughout motion, car A should have greater instanteneous velocity at t1.

Correct. Car A can't pass Car B if they both have constant velocities and car B has a higher one.
also, it shouldn't matter if car B is accelerating and car A is traveling in a constant velocity.. right? since even though B is accelerating car A must have greater velocity at t1 in order to pass car B, therefore instanteneous of car A should still be greater. please correct me if I'm wrong. thank you
Car A can't pass Car B unless its velocity at the time of passing is greater, correct. However, there's no say as to what may happen later on:

The position equation for Car A and Car B are as follows:

$$x(t)_a = v_0t$$

$$x(t)_b = v_{0b} + \frac{at^2}{2}$$

It is very possible that the initial velocity of car B will be lower than Car A, at which point t=t1 car A will pass, but as t increases, the acceleration will eventually cause car B to pass car A again.

two cars A and B are traveling in a straight line. Car A is passing car B and at time t1, car A is adjacent to car B. If each cars are traveling in a constant speed ( each with separate constant speed)

If each car is traveling at a constant speed as you say, then neither car is accelerating, which means that once car A passes car B, car B will not overtake car A again.

In fact, if both cars are traveling at constant speed, there is no need to talk about "instantaneous" velocity- instantaneious= average= constant speed will do nicely.

If B is accelerating, then you do need to say "instantaneous". Of course, knowing only the acceleration tells you nothing about the speed at a giving instant.

## 1. What is instantaneous velocity?

Instantaneous velocity is the rate of change of position at a specific moment in time. It is the velocity of an object at a given instant, rather than the average velocity over a period of time.

## 2. How is instantaneous velocity calculated?

Instantaneous velocity is calculated by finding the derivative of the position function with respect to time. This can be done using calculus or by finding the slope of the tangent line to the position-time graph at a specific point.

## 3. What is the difference between instantaneous velocity and average velocity?

The main difference between instantaneous velocity and average velocity is the time frame over which the velocity is measured. Average velocity is calculated over a period of time, while instantaneous velocity is measured at a specific moment in time. Average velocity gives an overall picture of an object's motion, while instantaneous velocity provides information about its motion at a specific point.

## 4. Can instantaneous velocity be negative?

Yes, instantaneous velocity can be negative. This means that the object is moving in the opposite direction of its positive velocity. For example, if an object is moving with a velocity of 5 m/s in the positive direction, its instantaneous velocity at a specific point in time may be -3 m/s if it is moving in the negative direction at that moment.

## 5. What is the significance of instantaneous velocity in physics?

Instantaneous velocity is an important concept in physics as it helps us understand the motion of objects in detail. It allows us to analyze an object's motion at a specific moment and make predictions about its future motion. It is also used in calculus and other mathematical applications to solve problems related to motion and change.

• Introductory Physics Homework Help
Replies
11
Views
975
• Introductory Physics Homework Help
Replies
57
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
467
• Introductory Physics Homework Help
Replies
6
Views
172
• Introductory Physics Homework Help
Replies
6
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
808
• Introductory Physics Homework Help
Replies
3
Views
689
• Introductory Physics Homework Help
Replies
13
Views
366
• Introductory Physics Homework Help
Replies
7
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
1K