How to Correctly Check if a Process is running and Stop it

If you don't need to display exact result "running" / "not runnuning", you could simply:

ps notepad -ErrorAction SilentlyContinue | kill -PassThru

If the process was not running, you'll get no results. If it was running, you'll receive get-process output, and the process will be stopped.

The way you're doing it you're querying for the process twice. Also Lynn raises a good point about being nice first. I'd probably try something like the following:

# get Firefox process
$firefox = Get-Process firefox -ErrorAction SilentlyContinue
if ($firefox) {
  # try gracefully first
  $firefox.CloseMainWindow()
  # kill after five seconds
  Sleep 5
  if (!$firefox.HasExited) {
    $firefox | Stop-Process -Force
  }
}
Remove-Variable firefox