Question

If the speed of light is $3.0\times {{10}^{8}}m{{s}^{-1}}$, calculate the distance covered by light in 2.00ns.

Answer 1

Hint: Recollect the basic concepts. We have been the speed of light in meters per second. We need to calculate the distance covered by light in 2 nanoseconds. Find out the conversion factor between one second and one nanosecond. Then use the formula, $\text{speed=}\dfrac{\text{distance}}{\text{time}}$ and just substitute the values and calculate the distance covered to get the answer.

Complete step by step solution:
- Speed of light is the distance covered by light in unit time.
- Speed is given by the formula,
\[\text{Speed =}\dfrac{\text{distance}}{\text{time}}\]
- We have been given speed of light in meters per second that is, $3.0\times {{10}^{8}}m{{s}^{-1}}$. We need to calculate the distance covered by light in 2ns. So, time taken by light to cover a certain distance is 2ns.
- Therefore, $\text{Distance = Speed }\!\!\times\!\!\text{ Time}$ ……(1)
- Now, speed of light is given in terms of meter per second but time is given in terms of nanoseconds.
- We know that, $1ns={{10}^{-9}}s$ and therefore, $time=2ns=2\times {{10}^{-9}}s$
- Substituting the values of speed and time in equation (1) we get,
\[\begin{align}
  & \text{Distance = Speed }\!\!\times\!\!\text{ Time} \\
 & \text{=3}\times \text{1}{{\text{0}}^{8}}m{{s}^{-1}}\times 2\times {{10}^{-9}}s \\
 & =0.6m
\end{align}\]
- Therefore, the distance covered by light in 2ns is 0.6meter.

- Hence, if the speed of light is $3.0\times {{10}^{8}}m{{s}^{-1}}$, then the distance covered by light in 2.00ns is 0.6m.

Note: Remember light travels at the speed of 3lakh kilometres per second or $3.0\times {{10}^{8}}m{{s}^{-1}}$. Speed of light is defined as the distance covered by light per unit time. It is a directionless quantity. Velocity is analogous to speed which is displacement per unit time but it is a vector quantity and has a particular direction.