An object travels North at #15 m/s# for #2 s# and then travels South at #2 m/s# for #8 s#. What are the object's average speed and velocity?
speed = 4.6 m/s
velocity = 1.4 m/s (north) or -1,4m/s (south)
Now that we are aware of the differences between speed and velocity, we must make that distinction.
however,
Disposition is a vector quantity, whereas distance is a scalar quantity, hence the two are not the same.
Since scalar quantities lack direction, calculations are performed without them.
However, direction affects vector quantities, so we must verify the directions in our computations.
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The object's average speed is ( \frac{{\text{{total distance}}}}{{\text{{total time}}}} = \frac{{(15 , \text{m/s} \times 2 , \text{s}) + (2 , \text{m/s} \times 8 , \text{s})}}{{2 , \text{s} + 8 , \text{s}}} = \frac{{30 , \text{m} + 16 , \text{m}}}{{10 , \text{s}}} = \frac{{46 , \text{m}}}{{10 , \text{s}}} = 4.6 , \text{m/s}). The object's average velocity is ( \frac{{\text{{total displacement}}}}{{\text{{total time}}}} = \frac{{0 , \text{m/s} - 15 , \text{m/s}}}{{2 , \text{s} + 8 , \text{s}}} = \frac{{-15 , \text{m/s}}}{{10 , \text{s}}} = -1.5 , \text{m/s}).
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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.
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.
- If a projectile is shot at an angle of #(5pi)/12# and at a velocity of #1 m/s#, when will it reach its maximum height??
- An object's two dimensional velocity is given by #v(t) = ( 3t^2 - 2t , 1- 3t )#. What is the object's rate and direction of acceleration at #t=4 #?
- An object's velocity is given by #v(t) = (2t^2 +t +1 , sin2t )#. What is the object's rate and direction of acceleration at #t=6 #?
- A uniformly accelarating object covers a distance of #11# meters in #6.5# seconds. If it reaches a final velocity of #3.3# m/sec, what is its initial velocity?
- What is the average speed of an object that is moving at #8 m/s# at #t=0# and accelerates at a rate of #a(t) =5-2t# on #t in [0,3]#?

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