Derivation of Distance to Get Velocity and Acceleration
Derivatives reveal a new connection between distance , velocity and acceleration . By differentiating, you can find an expression for velocity and acceleration using the provided distance . This is how they are connected:
If you have the position (distance) , then it follows that
A plane flies from London to New York. The aircraft’s position above theAtlantic is given by
where is the number of hours after departure, and the unitofiskilometers.
You insert into :
After four hours, the plane has flown km.
To find the velocity of the plane after four hours, you have to find the velocity of the plane. You find that by differentiating :
After four hours, the velocity of the plane is about km/h.
To find out what the acceleration is after four hours, you have to differentiate the velocity function . That gives you
After four hours, the acceleration of the plane is km/h2. This tells you that the plane is increasing its speed four hours into the flight.