An electron, starting from rest and moving
with a constant acceleration, travels 5.8 cm in
14 ms.
What is the magnitude of this acceleration?
Answer in units of km/s2
To find the magnitude of acceleration, we can use the kinematic equation:
\[ s = ut + \frac{1}{2}at^2 \]
where:
s = displacement
u = initial velocity (in this case, the electron starts from rest, so u = 0)
t = time taken
a = acceleration
Given:
s = 5.8 cm = 0.058 m (converted from cm to m)
t = 14 ms = 0.014 s (converted from ms to s)
u = 0
Rearranging the equation, we have:
\[ a = \frac{2(s - ut)}{t^2} \]
Substituting the given values:
\[ a = \frac{2(0.058 - 0 \cdot 0.014)}{0.014^2} \]
\[ a = \frac{0.116}{0.000196} \]
\[ a = 591.84 \, \text{m/s}^2 \]
To convert m/s^2 to km/s^2, we divide by 1000:
\[ \text{Magnitude of acceleration} = \frac{591.84}{1000} \, \text{km/s}^2 \]
\[ \text{Magnitude of acceleration} = 0.59184 \, \text{km/s}^2 \]
Therefore, the magnitude of acceleration is 0.59184 km/s^2.