Answer:
Acceleration of this electron: [tex]-5.60 \times 10^{15}\; \rm m \cdot s^{-2}[/tex].
Time taken: approximately [tex]9.39 \times 10^{-9}\; \rm s[/tex].
Explanation:
- Let [tex]u[/tex] denote the velocity of this electron before the change.
- Let [tex]v[/tex] denote the velocity of this electron after the change.
- Let [tex]x[/tex] denote the displacement.
- Let [tex]a[/tex] denote the acceleration.
- Let [tex]t[/tex] denote the time taken.
Apply the SUVAT equation that does not involve time:
[tex]v^{2} - u^{2} = 2\, a \, x[/tex].
Equivalently:
[tex]\begin{aligned}a &= \frac{v^{2} - u^{2}}{2\, x}\end{aligned}[/tex].
By this equation, the acceleration of this electron would be:
[tex]\begin{aligned}a &= \frac{v^{2} - u^{2}}{2\, x} \\ &= \frac{(7.72 \times 10^{7}\; \rm m \cdot s^{-1})^{2} - (2.46 \times 10^{7} \; \rm m \cdot s^{-1})^{2}}{2 \times 0.478\; \rm m} \\ &\approx -5.60 \times 10^{15}\; \rm m \cdot s^{-2}\end{aligned}[/tex].
The speed of this electron has changed from [tex]u = 7.72 \times 10^{7}\; \rm m\cdot s^{-1}[/tex] to [tex]v = 2.46 \times 10^{7}\; \rm m \cdot s^{-1}[/tex]. Calculate the time required to achieve this change at a rate of [tex]a \approx -5.60 \times 10^{15}\; \rm m\cdot s^{-2}[/tex]:
[tex]\begin{aligned}t &= \frac{v - u}{a} \\ &\approx \frac{2.46\times 10^{7}\; \rm m \cdot s^{-1} - 7.72 \times 10^{7}\; \rm m\cdot s^{-1}}{-5.60 \times 10^{15}\; \rm m\cdot s^{-2}} \\ &\approx 9.39 \times 10^{-9}\; \rm s\end{aligned}[/tex].
