The instantaneous velocity is the velocity (both magnitude and direction) that s

Question

The instantaneous velocity is the velocity (both magnitude and direction) that something has at any instant of time. The earth travels around the sun in a year. The radius of the earth's orbit is 1.50 X 10^11 m (150,000,000,000 m). The distance of the earth to the sun is called one Astronomical Unit (A.U.) It takes one year for the earth to travel around the sun. The average velocity of the earth after exactly one year is Question 26 options: 30. km/s 3.0 km/s 1 km/s The average velocity is zero.

Explanation / Answer

You're right. The only difference between intantaneous speed and instantaneous velocity is that speed is a scalar and velocity is a vector. In oversimplified math terms, you can think of speed as the absolute value of the velocity vector's magnitude. In order to get instantaneous velocity, you must be given a position function. The time derivative of this position function will give you a velocity function. When you plug in any value of time, you will get the instantaneous velocity for that moment in time. Taking the absolute value of this number gives you instantaneous speed. If you want instantaneous acceleration, take the time derivative of the velocity function. Instantaneous acceleration is the value of your acceleration function at any point in time. Instantaneous acceleration is a vector, and there is no corresponding scalar quantity. A positive instantaneous acceleration tells you how much you have sped up at the instant (or at what rate your velocity has increased). A negative instantaneous acceleration tells you how much you have slowed down at that instant (or at what rate your velocity has decreased).

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