Instantaneous velocity Definition and 115 Threads

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...

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...

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...

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...

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?

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...

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...

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}## ...

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)}...

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?

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...

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...

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...

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...

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...

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...

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...

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 ?

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...

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...

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...

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...

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...

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...

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 =...

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...

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...

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?

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

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

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...

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.

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

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...

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 +...

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...

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

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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