Question

A highway police radar operating at 10 GHz observes a Doppler shift of 1,500 Hz when the radar is pointed at a moving car. What is the radial speed of the car toward the radar in miles per hour?

Answer 1

A radar emits waves. The waves reflect from a barrier (the car). Since the car moves, the incident waves reflect with some additional shift, which causes Doppler shift.

$$f=f_0\bigg(1+\frac vc\bigg), [f>f_0]\\\space\\ v=\frac{c(f-f_0)}{f_0}=\frac{c\Delta f}{f_0},\\\space\\ v=\frac{3\cdot10^8\cdot1500}{10\cdot10^9}=45\text{ m/s}.$$

45 m/s is 162 km/h.