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Ksju [112]
3 years ago
6

A particle moves along the x axis from the origin. The magnitude of the position vector at time t is

Physics
1 answer:
Maurinko [17]3 years ago
6 0

1) The average velocity is -2.1\cdot 10^5 m/s

2) The instantaneous velocity is 64t-260t^3

Explanation:

1)

The average velocity of an object is given by

v=\frac{d}{t}

where

d is the displacement

t is the time elapsed

In this problem, the position of the particle is given by the function

x(t) = 32t^2 - 65t^4

where t is the time.

The position of the particle at time t = 6 sec is

x(6) = 32(6)^2 - 65(6)^4=-83,088 m

While the position at time t = 12 sec is

x(12)=32(12)^2-65(12)^4=-1,343,232 m

So, the displacement is

d=x(12)-x(6)=-1,343,232-(-83,088)=-1,260,144 m

And therefore the average velocity is

v=\frac{-1,260,144 m}{12 s- 6 s}=-2.1\cdot 10^5 m/s

2)

The instantaneous velocity of a particle is given by the derivative of the position vector.

The position vector is

x(t) = 32t^2 - 65t^4

By differentiating with respect to t, we find the velocity vector:

v(t) = x'(t) = 2\cdot 32 t - 4\cdot 65 t^3 = 64t - 260 t^3

Therefore, the instantaaneous velocity at any time t can be found by substituting the value of t in this expression.

Learn more about velocity:

brainly.com/question/5248528

#LearnwithBrainly

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