an electorn is 20 ccom away from a fixed point charge , q =-0.250uc . if it starst to move from rest , then how fast will it be moving when it is a t distance ?
Well, let's see. An electron starts from rest and moves towards a fixed point charge. To find out how fast it will be moving at a certain distance, we can use the good ol' Coulomb's Law and some math.
But hey, let's have a little fun with it too! Imagine the electron is in a hurry to meet its charge buddy, so it starts running.
Now, according to Coulomb's Law, the force between two charges is given by:
\[ F = k \frac{q_1 q_2}{r^2} \]
Where F is the force, k is the electrostatic constant, q_1 and q_2 are the charges, and r is the distance between them.
Since the electron has a negative charge, the force acting on it will be attractive towards the fixed point charge. So, it will be pulling the electron in.
Now, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration:
\[ F = m \cdot a \]
Here, m is the mass of the electron, and a is its acceleration.
Now, let's solve for acceleration:
\[ a = \frac{F}{m} \]
Substituting Coulomb's Law equation into Newton's second law, we get:
\[ a = \frac{k \frac{q_1 q_2}{r^2}}{m} \]
Now, we can use the kinematic equation to find the final velocity of the electron at a certain distance:
\[ v^2 = u^2 + 2aS \]
Where v is the final velocity, u is the initial velocity (which is 0 since the electron starts from rest), a is the acceleration, and S is the distance traveled.
Since the initial velocity is 0, the equation simplifies to:
\[ v^2 = 2 a S \]
Now we can substitute our expression for acceleration:
\[ v^2 = 2 \frac{k \frac{q_1 q_2}{r^2}}{m} S \]
Alrighty, now we can plug in the values you provided and solve for v. Just remember, this is a simplified model, and in reality, we would need to take into account other factors like electromagnetic fields and relativistic effects. But hey, we're just clowning around with physics here!
So, let's crunch the numbers and find out how fast our ambitious electron will be moving when it reaches distance t from the fixed point charge.