An electron has an initial speed of
2.95 × 105 m/s.If it undergoes an acceleration of 2.7 × 1014 m/s^2, how long will it take to reach a speed of 5.94 × 105 m/s?
What about how far it has traveled in the time
luckily 6*10^5 is much less than light speed of 3*10^8 so not a relativity problem
v = Vi + a t
5.94 * 10^5 = 2.95*10^5 + 2.7*10^14 t
divide by 10^5
5.94 = 2.95 + 2.7*10^9 t
2.7 * 10^9 t = 2.99
t = 1.107 * 10^-9 seconds
To find the time it takes for the electron to reach a speed of 5.94 × 10^5 m/s, you can use the formula:
vf = vi + at
Where:
vf = final velocity = 5.94 × 10^5 m/s
vi = initial velocity = 2.95 × 10^5 m/s
a = acceleration = 2.7 × 10^14 m/s^2
t = time
Rearranging the formula, we have:
t = (vf - vi) / a
Substituting the given values, we get:
t = (5.94 × 10^5 m/s - 2.95 × 10^5 m/s) / (2.7 × 10^14 m/s^2)
Calculating it:
t = 3.99 × 10^5 m/s / (2.7 × 10^14 m/s^2)
Simplifying it further:
t ≈ 1.48 × 10^-9 seconds
Therefore, it will take approximately 1.48 × 10^-9 seconds for the electron to reach a speed of 5.94 × 10^5 m/s.
To find the time it takes for the electron to reach a speed of 5.94 × 10^5 m/s, we can use the equation of motion:
v = u + at
where:
v = final velocity (5.94 × 10^5 m/s)
u = initial velocity (2.95 × 10^5 m/s)
a = acceleration (2.7 × 10^14 m/s^2)
t = time
Rearranging the equation, we have:
t = (v - u) / a
Substituting the given values, we get:
t = (5.94 × 10^5 m/s - 2.95 × 10^5 m/s) / (2.7 × 10^14 m/s^2)
Now, let's calculate:
t = (2.99 × 10^5 m/s) / (2.7 × 10^14 m/s^2)
To simplify the calculation, we can write the powers of 10 in scientific notation:
t = (2.99 / 2.7) × (10^5 / 10^14) s
Dividing the numbers outside the powers of 10:
t = 1.107 × 10^(-9) s
Therefore, it will take approximately 1.107 × 10^(-9) seconds for the electron to reach a speed of 5.94 × 10^5 m/s.