First, if it shears (switches rapidly), you will lose indicated airspeed. This is because the air that blew into the pitot tube, which is used to measure indicated airspeed, has been reduced by the switch.
Secondly, your groundspeed will increase. The instrument in the airplane measures your airspeed as calculated by air blowing into the pitot tube. It does not account for changes in air density and is not the real speed the airplane is flying through the air. We call that speed True Airspeed. It measures how fast you would travel in still air. Now, with the wind blowing behind you, you move faster (relative to the ground) with a tailwind, just as a sailboat moves faster with the wind than into the wind. That is called groundspeed.
Long story short: Your groundspeed would increase, while indicated airspeed should decrease.
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More people are killed by donkeys than in airplane crashes each year....
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