# What is the difference between instantaneous velocity and speed?

Velocity is a vector and speed is a magnitude.

Recall that a vector has direction and magnitude. Speed is simply the magnitude. Direction can be as simple as positive and negative. Magnitude is always positive.

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Instantaneous velocity refers to the rate of change of position of an object at a specific moment in time, including both the magnitude and direction. Speed, on the other hand, refers to the rate at which an object covers distance, irrespective of direction. In essence, instantaneous velocity accounts for both speed and direction, whereas speed only considers the magnitude of motion.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How does the derivative relate to the tangent line?
- What is the equation of the line tangent to #f(x)=x ^2cos^2(2x) # at #x=pi/4#?
- What is the equation of the normal line of #f(x)=cos(2x-pi/2)# at #x=pi/6#?
- Consider the function #f(x)=3x^3–2x# on the interval [–4, 4], how do you find the average or mean slope of the function on this interval?
- Can the instantaneous rate of change be zero?

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