Instantaneous Velocity of a electron with a provided formula

In summary, the motion of an electron is described by the equation 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. To find the velocity at different times, we use the equation v=dx/dt and take the derivative of the position equation. Plugging in the given values for p, q, and r, we can find the instantaneous velocity at t=0s, t=1s, t=2s, and t=3s to be 0 m/s, 9.4 m/s, 6.6 m/s, and -40
  • #1
Flinze
23
1

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 which for a) i got +9 b)8.4 c)-1 d)-30.6
At this point I'm not sure what to do, and I'm totally lost...
 
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  • #2
Flinze said:

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 which for a) i got +9 b)8.4 c)-1 d)-30.6
At this point I'm not sure what to do, and I'm totally lost...

Whoever told you that v = x/t? That is almost always false! That is why Newton (or maybe Leibniz) invented calculus, and why you had to learn it.
 
  • #3
Ray Vickson said:
Whoever told you that v = x/t? That is almost always false! That is why Newton (or maybe Leibniz) invented calculus, and why you had to learn it.

Would it be v=d/t?
 
  • #4
Flinze said:
Would it be v=d/t?
You're overlooking some obvious hints here.
1. instantaneous velocity
2. calculus
 
  • #5
you are probably talking about v=dx/dt
 
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  • #6
I haven't learned how to take derivatives yet using Calculus, my Calculus course just started and we haven't covered much so far. Is there possibly another way of solving this without the use of Calculus?
 
  • #7
i don't think so o_O
that is really wierd... you teachers should be more carefull.. you sure you didn't even touched derivatives while learning kinematics?
 
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  • #8
WrongMan said:
i don't think so o_O
that is really wierd... you teachers should be more carefull.. you sure you didn't even touched derivatives while learning kinematics?

100% we haven't yet... This and another question that is also part of my assignment asks the same thing..
 
  • #9
Okay, I searched up on YouTube on how to take derivatives, so I took the derivative of my equation in which it becomes x'(t)=3pt^2+2qt+0. Afterwards I plugged in the time into the t's and got my answer! Thanks WrongMan by helping me "accidentally" find what derivatives are when I tried searching up the meaning of v=dx/dt
 

Related to Instantaneous Velocity of a electron with a provided formula

What is the formula for calculating instantaneous velocity of an electron?

The formula for calculating instantaneous velocity of an electron is v = dx/dt, where v is the instantaneous velocity, dx is the change in position, and dt is the change in time.

What is the unit of measurement for instantaneous velocity of an electron?

The unit of measurement for instantaneous velocity of an electron is meters per second (m/s).

How is instantaneous velocity different from average velocity?

Instantaneous velocity is the velocity of an object at a specific moment in time, while average velocity is the total distance traveled divided by the total time taken. Instantaneous velocity can change at different points in time, while average velocity remains constant over the entire time period.

What factors can affect the instantaneous velocity of an electron?

The instantaneous velocity of an electron can be affected by external forces, such as electric or magnetic fields, as well as the electron's own inertia and the properties of the material it is traveling through.

How is the instantaneous velocity of an electron measured in experiments?

The instantaneous velocity of an electron can be measured using various techniques, such as time-of-flight measurements, velocity mapping spectroscopy, and electron energy-loss spectroscopy. These techniques use the principles of electromagnetism and quantum mechanics to accurately measure the velocity of an electron.

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