Two charged particles in an accelerator are at rest until an electric field causes them to accelerate away from each other when the field switched is turned on, particle a accelerates to the left at 8.97e+07 m/s2 while particle B accelerates to the right at 7.78e+08 they start moving at the same time. Some time after the field is switched on, the particles will be 135 m apart.
I don't see a question here. Do they want to now when the particles are that far apart?
The distance the two particles are apart is (1/2)(a1 + a2)t^2, since they go in opposite directions, if you use positive values for both a1 and a2.
sorry,
How long after the field is switched on are the particles 135 m apart?
B. How far has each particle moved in this time?
C. How fast is each particle moving at this time?
should i still use that formula
To find the time it takes for the particles to be 135 m apart, we can use the equations of motion for uniformly accelerated particles.
First, let's calculate the time it takes for particle A to reach a velocity of 0 m/s, assuming it started with an initial velocity of 0 m/s and accelerated at a rate of -8.97e+07 m/s^2 (since it accelerates to the left). We can use the equation:
v = u + at
Where:
v = final velocity (0 m/s)
u = initial velocity (0 m/s)
a = acceleration (-8.97e+07 m/s^2)
0 = 0 + (-8.97e+07)t
t = 0 / (-8.97e+07)
t = 0 s
So, it takes 0 seconds for particle A to reach a velocity of 0 m/s.
Now, let's find the distance covered by particle A in this time. We can use the equation:
s = ut + (1/2)at^2
Where:
s = distance covered
u = initial velocity (0 m/s)
t = time (0 s)
a = acceleration (-8.97e+07 m/s^2)
s = (0)(0) + (1/2)(-8.97e+07)(0)^2
s = 0
Therefore, particle A covers 0 meters during this time.
Next, we can calculate the time it takes for particle B to reach a velocity of 0 m/s, assuming it started with an initial velocity of 0 m/s and accelerated at a rate of 7.78e+08 m/s^2 (since it accelerates to the right). Using the equation:
v = u + at
Where:
v = final velocity (0 m/s)
u = initial velocity (0 m/s)
a = acceleration (7.78e+08 m/s^2)
0 = 0 + (7.78e+08)t
t = 0 / (7.78e+08)
t = 0 s
So, it takes 0 seconds for particle B to reach a velocity of 0 m/s.
Similarly, particle B covers 0 meters during this time.
Since both particles start moving at the same time, the distance between them remains unchanged at 135 m throughout the time of their motion. Therefore, there is no need to calculate the time it takes for them to be 135 m apart because they are always 135 m apart.