a) The acceleration of the proton is [tex]5.0\cdot 10^{13} m/s^2[/tex]
b) The time required to reach the given velocity is [tex]2\cdot 10^{-8}s[/tex]
Explanation:
a)
This is a motion at constant acceleration, so we can use the following suvat equation:
[tex]v^2-u^2=2as[/tex]
where
v is the final velocity
u is the initial velocity
a is the acceleration
s is the distance covered
For the proton in this problem, we have:
[tex]v=1,000,000 m/s[/tex] is the final velocity
[tex]u=0[/tex] is the initial velocity (it starts from rest)
[tex]s = 0.01 m[/tex] is the distance covered
Solving for a, we find the acceleration:
[tex]a=\frac{v^2-u^2}{2s}=\frac{(1,000,000)^2-0}{2(0.01)}=5.0\cdot 10^{13} m/s^2[/tex]
b)
For this part, we can use the following suvat equation instead:
[tex]v=u+at[/tex]
where:
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time taken for the velocity to change from u to v
We have here the following data:
[tex]v=1,000,000 m/s[/tex] is the final velocity
[tex]u=0[/tex] is the initial velocity (it starts from rest)
[tex]a=5.0\cdot 10^{13} m/s^2[/tex]
Solving for t, we find
[tex]t=\frac{v-u}{a}=\frac{1,000,000}{5.0\cdot 10^{13}}=2\cdot 10^{-8}s[/tex]
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