A radar signal is beamed toward a planet from earth and is echo is received seven minutes later.The distance between the planet and the earth is 0.00000000063m find the velocity of the signal

The echo is received seven minutes later, so the total time taken for the signal to travel to the planet and back is $t = 7\text{ minutes}$.

$$t = 7\text{ minutes} \times 60\ \frac{\text{s}}{\text{minute}} = 420\text{ s}$$

The distance between the Earth and the planet is given as $d = 0.00000000063\text{ m}$.
The radar signal travels from Earth to the planet and then the echo travels back from the planet to Earth. Therefore, the total distance covered by the signal is twice the distance between the Earth and the planet.

$$\text{Total distance} = 2 \times d$$ $$\text{Total distance} = 2 \times 0.00000000063\text{ m} = 0.00000000126\text{ m}$$

Velocity is calculated as total distance divided by total time.

$$\text{Velocity} = \frac{\text{Total distance}}{\text{Total time}}$$ $$v = \frac{0.00000000126\text{ m}}{420\text{ s}}$$ $$v = 3.0 \times 10^{-12}\ \frac{\text{m}}{\text{s}}$$

The velocity of the signal is:

$$3.0 \times 10^{-12}\ \frac{\text{m}}{\text{s}}$$