Instantaneous velocity Definition and 115 Threads

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction of motion (e.g. 60 km/h to the north). Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.
Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object has a changing velocity and is said to be undergoing an acceleration.

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  1. A

    I Instantaneous velocity - displacement and distance

    Instantaneous velocity is defined as the first derivative of displacement with respect to time: ##\vec{v} = \dfrac{d \vec{r}}{dt}## However, instantaneous velocity is also defined as the first derivative of function of distance with respect to time: ##v = \dfrac{ds}{dt}## Why do these two...
  2. A

    B Understanding the instantaneous velocity formula

    If the formula for instantaneous velocity is: ##v = \lim_{\Delta t \to 0} \dfrac{\Delta s}{\Delta t}## Why the result of equation isn’t infinity? It’s said that if we divide something by number very close to zero, it results in infinitely large number. But how does this equation work then? It...
  3. Sciencemaster

    I Is an accelerating frame the same as an inertial frame at a point?

    If we have an observer that is accelerating in one direction (perhaps a rocket ship accelerating towards the sun), would its reference frame be identical to an observer at the same point that is not accelerating, but has the same instantaneous velocity? In other words, is an accelerating...
  4. Clockclocle

    I When does the instantaneous velocity exist?

    The instantaneous velocity at time a is defined as derivative of motion function f(t). It is not similar to average velocity in an interval of time. From the Newton law. If an object is at rest, we must exert a force to make it move, assume that there is no friction. Depend on the weight of...
  5. L

    Average velocity and instantaneous velocity

  6. W

    MHB Advanced Functions Average vs. Instantaneous velocity

    What do the average velocities on the very short time intervals [2,2.01] and [1.99,2] approximate? What relationship does this suggest exist between a velocity on an interval [a,b] and a velocity near t=a+b/2 for this type of polynomial?
  7. K

    Can instantaneous velocity be different from average velocity?

    Homework Statement Is it possible for the instantaneous velocity of an object at some time, t1, to not be parallel to the average velocity over a short time interval, Δt=t2-t1? If it is not possible, explain why not. If it is possible, explain what this situation implies about the motion of...
  8. fight_club_alum

    How Do You Calculate Instantaneous Velocity at a Midpoint in Particle Motion?

    Homework Statement The position of a particle moving along the x axis is given in centimeters by x = 9.35 + 1.03 t3, where t is in seconds. Calculate the instantaneous velocity when the particle is midway between its positions at t = 2.00 s and t = 3.00 s. Homework EquationsThe Attempt at a...
  9. Arman777

    How to Find Instantaneous Velocity Using Force

    Homework Statement Let's suppose we have two objects on ##x## axis.They have mass ##m## and ##M##, They are exerting a gravitational force on each other and its magnitude can be written as ##F=\frac {mMG} {R^2}##. So my question is can we find Instantaneous velocity of ##m##, ##{V_m}## ...
  10. F

    Instantaneous velocity calculation from position data

    Hello Forum, Given position and related time data, what is the most correct way to calculate the instantaneous speed? For example, given the data (x1, t1) , (x2, t2), (x3, t3) , (x4, t4), (x5, t5), is the instantaneous speed at time t3 given more correctly by v(t_3) = \frac{(x_4-x_2)}...
  11. Biscuit

    Calculate Instantaneous Velocity at t=2s

    Homework Statement Homework EquationsThe Attempt at a Solution I tried to find the slope of the tangent line, but this gave me 3.66 and the answer is 3.8 how do I find this?
  12. O

    Difference between instantaneous velocity and acceleration

    Hi, I'm just beginning to learn physics on my own. It seems that instantaneous velocity and acceleration are the same thing. Is it reasonable for me to be confused about the two? If acceleration = final velocity - initial velocity / change in time ... then how this any different from...
  13. FritoTaco

    Estimate Instantaneous Velocity

    Homework Statement If a ball is thrown into the air with a velocity of 48 ft/s, its height in feet t seconds later is given by y = 48t − 16t2. (a) Find the average velocity for the time period beginning when t = 2 and lasting for each of the following. (i) 0.5 seconds (ii) 0.1 seconds...
  14. pravignya raj

    Instantaneous Velocity: Can We Find it at a Point?

    1.one question i have just read n my book that find inst. velocity at a point ? i think it is a wrong quotation since we need atleast two points for measuring dx length so my teacher taught me that assume point p where we have to find inst. velocity thank take one point before and after p that...
  15. U

    Quick question about instantaneous velocity and acceleration

    Homework Statement [/B] Homework Equations The Attempt at a Solution [/B] Hey, I did part a and b. Although I need a little help with part c. I know you're supposed to solve for t^2 but I don't know what value to use for acceleration. I'd use the quadratic formula to solve for t^2, but...
  16. I

    Instantaneous Speed = Instantaneous Velocity?

    Hi everyone, I am taking my first physics class (algebra based), and yesterday we were covering 1-Dimensional motion. I'm enrolled in Cal. 2, so I have some understanding of instantaneous velocity, etc. However, my professor said that instantaneous speed is always equal too instantaneous...
  17. Flinze

    Instantaneous Velocity of a electron with a provided formula

    Homework Statement The motion of an electron is given by x(t)=pt^3 +qt^2 +r, with p = -1.9 m/s^3 , q = +1.3 m/s^2 , and r = +9.0 m. What is the velocity at: a) t=0s b) t=1s c) t=2s d t=3s Homework Equations v=x/t The Attempt at a Solution I have tried plugging in the time to equal to t, in...
  18. toboldlygo

    Instantaneous Velocity from Strobe Diagram

    Hi guys! My first post here. I've been frequenting Physics Forums and have found a wealth of information, and I'm hoping I can get some specific help about this concept. Thanks! Homework Statement "Cart A and B move along a horizontal track. The top-view strobe diagram below shows the...
  19. I

    Average Velocity and Final Instantaneous Velocity

    Suppose a body moving in a curved path at a constant speed would its average velocity for a specific time period equal its final instantaneous velocity at the end of this period ?
  20. M

    How Far Ahead Should You Monitor for Obstacles When Controlling a Mars Rover?

    You sit at NASA to control the Mars rover across the Martian surface 2.0 x 10^8 km away. The communication travels at the speed of light between Earth and Mars, and the rover's top speed is 2.0 m/min. How far ahead in the rover's field of view you have to watch out for a Martian cliff? My first...
  21. VaioZ

    Instantaneous Velocity and Acceleration

    Homework Statement A car is stopped at a traffic light. It then travels along a straight road so that its velocity is given by the equation v(t)=(7.20m/s^2)t-(0.720m/s^3)t^2 Determine the following a. The average velocity of the car from t=0s to t=10s b. The instantaneous velocity of the car at...
  22. M

    Instantaneous velocity when non-constant acceleration

    Hello. I've seen on Wikipedia (http://en.wikipedia.org/wiki/Airsoft_pellets#pellet_ballistics) a formula to find the aerodynamic drag (velocity dependent negative acceleration) for a spherical body. Knowing body's mass, diameter and air density I simplified it to the form: A = vt2 * 0.04 where A...
  23. F

    Using v= omega cross r to find instantaneous velocity

    Homework Statement An object is rotating at 4 rad/s about an axis in direction of (2 \hat{i} - 4 \hat{j} + 3\hat{k} ) which then passes through a point (1,2,0)m . Calculate the instantaneous velocity at the point (2,0,3)m (Hint: use \vec{v} = \vec{\omega} \times \vec{r} )Homework Equations...
  24. C

    Determine the Magnitude of the instantaneous Velocity

    Homework Statement Determine the Magnitude of the instantaneous velocity at T=5s Function is x=AT^2 + B A=2.1m/s^2 B=2.8 M Homework Equations The previous questions answered on this problem are: AVG Velocity is 16.8 Displacement is 33.6 from 3s to 5s The Attempt at a Solution I'm not sure how...
  25. J

    What is the Instantaneous Velocity Question and How to Solve It?

    Homework Statement I am having trouble with the last question my teacher gave me. I have attached a picture. It is about instantaneous velocity. I did the same thing for all the other questions?[/B] Homework Equations average velocity = delta x / delta tThe Attempt at a Solution I did...
  26. C

    Instantaneous velocity and a catapult

    Homework Statement A stone of mass 5 g is projected with a rubber catapult. If the catapult is streched through a distance of 7 cm by an average force of 70 N, calculate the instantaneous velocity of the stone when released. Homework Equations work done in elastic material w = 1/2 fe =...
  27. S

    Finding the instantaneous velocity of a scalar function?

    Homework Statement Find the instantaneous velocity of f(x, y, z) = xyz, at (1, 2, 1) Homework Equations The Attempt at a Solution I think this problem our proffesor gave us wasn't formulated correctly. The only time when we calculated instantaneous velocity was when we had a...
  28. N

    Kinematics motion-setting up instantaneous velocity function

    Homework Statement An object starts moving in a straight line from position xi, at time t =0, with velocity vi. Its acceleration is given by a = ai + bt, where ai and b are constant. Find expressions for a)instantaneous velocity b) position as functions of time. Homework Equations...
  29. P

    MHB What is the meaning of instantaneous velocity and how is it defined?

    I'm not really sure how this concept makes sense. We give it meaning by way of a limit but, to my mind, at any instant the car is motionless so how can it have a velocity? What, in essence, does it mean to say that at some point in time a car is going 2 mph?
  30. S

    When can instantaneous velocity equal average velocity during a 10-second trip?

    The position of a particle moving in a straight line during a 10–second trip is s(t) = 3t2 − 3t + 5 cm.Find a time t at which the instantaneous velocity is equal to the average velocity for the entire trip
  31. MarkFL

    MHB Jaden Harris' Velocity Ques. at Yahoo Answers

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  32. M

    Trying to find instantaneous velocity at a point

    Homework Statement Given the function s(t) = -16t2 + 100t which represents the velocity of an object in meters, what is the instantaneous velocity at t = 3 seconds? Homework Equations I think these are correct: Average velocity equals the slope of the secant line connecting any two points...
  33. F

    What is the Instantaneous Velocity at t = 4.0s?

    Homework Statement Determine the instantaneous velocity at time t = 4, 0 s Homework Equations The Attempt at a Solution I believe it has something to do with the derivative of the point at t = 4.0s but I don't know how to solve this. I need some guidance.
  34. AakashPandita

    Confusion regarding notation of instantaneous velocity wrt something.

    I know that v(t)=dx/dt Then what is v(x) and how? Is it also dx/dt or something else?
  35. G

    Terminal Velocity Given Acceleration at Instantaneous Velocity

    Homework Statement This is a repost of a homework like question. The previous thread I did not understand. In the assumption that drag is proportional to velocity, and when v = 20 m/s, a = 7.35 m/s^2, find the terminal velocity. Homework Equations The thread stated that the equation most...
  36. P

    Find the instantaneous velocity

    Homework Statement a ball is thrown in the air. its height from the ground in metres after t seconds is modeled by h(t) = -5t^2 + 20t + 1. What is the instantaneous velocity of the ball at t=2 seconds? Homework Equations (f(a+h)-f(a))/h The Attempt at a Solution h(2) = -5(2)2 +...
  37. P

    Average and instantaneous velocity

    Homework Statement Given the following formula for distance, find the average velocity on the interval [1,3] S(t) = t/(1+t^2) Homework Equations Vavg = (S(t0) - S(t1)) / (t0 - t1) or Vavg = (V0 + V1)/2The Attempt at a Solution I get two different answers and I need help understand why...
  38. J

    Determine the Instantaneous Velocity of two coordinates on a graph

    I can't provide all the information, because I'm on my mobile phone. Here is a shot of the problem: The tangent of each curve is the slope, right? So how do we use that to find vf (instantaneous velocity) at 4s and 8s
  39. 0

    Derivation of Instantaneous Velocity

    Find the instantaneous velocity where r is the position vector as a function of time: r(t)=(3.0m/s^2)t\hat{x}+(4.0m/s)t\hat{y} I attempted to find the derivative of this to find instantaneous velocity, but the book's solution was different. I think the author of the book may have made a...
  40. R

    Instantaneous velocity in one dimension

    I started recently to study physics for motions, it is interesting so far but sadly I need some basic knowledge in calculus, I can get the Instantaneous velocity if the question gave me a function of time, but I don't know how to get it from a graph. I used the equation of calculating average...
  41. V

    Representing instantaneous velocity vs time on a graph

    Homework Statement I need to draw an instantaneous velocity vs time graph of an object moving at a constant velocity, provide an equation, and explain what it all means. I know that instantaneous velocity is typically shown as dx/dt (the derivative of change in position with respect to time...
  42. I

    Find the Instantaneous Velocity of D(x) = x + 2cos(x) in (0,2π)

    Homework Statement if d(x)=x+2cosx represents the distance traveled by a particle from x=0 to x= 2pi.Find an x value in (0,2pi) for which the instantaneous velocity equals the average velocity. The Attempt at a Solution This question is a direct application of the mean value...
  43. V

    Instantaneous velocity, help me please

    Homework Statement I need to find the instantaneous velocity directly before a car collides with another at an intersection. It travels 24 metres with an acceleration of -5.39 m s2. The only time factor given is the light sequence: Green for 45 seconds, amber for 3 seconds and red for 5...
  44. Z

    Instantaneous velocity of an object with varying mass at the bottom of a slope

    I conducted an experiment to investigate whether the mass of an object will affect the object speed at the bottom of a slope with a constant gradient. The experiment showed that as the mass of the object (car) increases, the speed of the car at the bottom of the slope increases. I still do not...
  45. K

    Instantaneous velocity from avg velocity with constant accelartion

    Homework Statement With constant acceleration prove that the average velocity from t1 to t2 =t1 + Δt is equal to the instanous velocity in the middle of the time interval between t1 and t2. Homework Equations What I am looking for is a general equation that does not involve accelaration. All I...
  46. A

    Instantaneous Velocity from the graph

    Homework Statement The problem is finding the instantaneous velocity during certain time intervals from the graph. Examples of time intervals: 1.1s, 7.4s, 2.7s Homework Equations I know this is the formula for finding the instantaneous velocity lim Δv=(Δx/Δt) t->0 The...
  47. C

    Instantaneous Velocity: drag racing problem

    The figure shows a graph of actual position-versus-time data for a particular type of drag racer known as a "funny car." Estimate the car's velocity at 2.0s Equation: v = m/s I thought I knew how to solve this, and I made a tangent line at the curve and 2s, and when I do the slope at...
  48. M

    Help finding instantaneous velocity graphically

    A graph of position versus time for a certain particle moving along the x-axis is shown in the figure below. Find the instantaneous velocity at the following instants. (a) t = 1.00 s (b) t = 3.00 s (c) t = 4.50 s (d) t = 7.50 s I know that a) is 5 m/s and c) is 0 m/s, but I need...
  49. P

    Effect of Instantaneous Velocity Change on Orbit

    Homework Statement A small particle of mass m is on a circular orbit of radius R around a much larger mass M. Suppose we suddenly increase the speed at which the mass m is moving by a factor (that is, v_{final} = α * v_{initial}, with α > 1). Compute the major axis, minor axis, pericentre...
  50. C

    What is the problem with this physics question?

    Homework Statement What is the instantaneous velocity of a freely falling object 19 s after it is released from a position of rest? The acceleration of gravity is 9.8 m/s^2 Answer in units of m/s Homework Equations Δv=aΔt The Attempt at a Solution 186.2
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