You are driving at 40 miles per hour and you speed up to 60 miles per hour over the course of 20 miles. How long were
1 answer:
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1) The average velocity is
2) The instantaneous velocity is
Explanation:
1)
The average velocity of an object is given by
where
d is the displacement
t is the time elapsed
In this problem, the position of the particle is given by the function
where t is the time.
The position of the particle at time t = 6 sec is
While the position at time t = 12 sec is
So, the displacement is
And therefore the average velocity is
2)
The instantaneous velocity of a particle is given by the derivative of the position vector.
The position vector is
By differentiating with respect to t, we find the velocity vector:
Therefore, the instantaaneous velocity at any time t can be found by substituting the value of t in this expression.
Learn more about velocity:
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