A plane flies from London to New York. The aircraft’s position above the Atlantic is given by |
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where is the number of hours after departure, and the unit of is kilometers.
- 1.
- How far has the plane flown after four hours?
- 2.
- What is the velocity of the plane after four hours?
- 3.
- Find the acceleration of the plane after four hours.
- 1.
- You insert into :
After four hours, the plane has flown km. - 2.
- 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. - 3.
- 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.