an electron starts from rest , travel a distance of 15cm with constant acceleration and hits a television screen at a speed of 3×10^6
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To determine the constant acceleration of the electron, we can use the formula for displacement:
\[s = ut + \frac{1}{2}at^2\]
where:
- \(s\) is the displacement
- \(u\) is the initial velocity (0 m/s since the electron starts from rest)
- \(a\) is the constant acceleration
- \(t\) is the time taken
We are given that the displacement \(s\) is 15 cm, which is equivalent to 0.15 m. The initial velocity \(u\) is 0 m/s. The final velocity \(v\) is \(3 \times 10^6\) m/s. We are trying to find the constant acceleration \(a\).
The final velocity of the electron can be related to the initial velocity and acceleration using the equation:
\[v = u + at\]
Since the electron starts from rest, we can simplify this equation to:
\[v = at\]
Solving for \(t\):
\[t = \frac{v}{a}\]
Substituting into the formula for displacement:
\[s = \frac{v}{a} \cdot v + \frac{1}{2} a \left(\frac{v}{a}\right)^2\]
Simplifying:
\[s = \frac{v^2}{a} + \frac{1}{2} \frac{v^2}{a}\]
Combining terms:
\[s = \frac{3}{2} \frac{v^2}{a}\]
Now we can rearrange the formula to solve for acceleration \(a\):
\[a = \frac{3}{2} \frac{v^2}{s}\]
Plugging in the values:
\[a = \frac{3}{2} \frac{(3 \times 10^6)^2}{0.15}\]
Using a calculator, we can find the value of acceleration.