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tara1brain2021

Answer:

This question is asking you to find the ending position of a shape (particle) that is moving horizontally along the horizontal axis by finding its velocity with the equation shown. When t=0, the shape is 4 units to the left of the vertical axis, so it wants you to find where on the horizontal axis the shape is when t = 8. Hope this helped!!!

MathPhys

Answer:

(C) 16 units to the right

Step-by-step explanation:

Position is the integral of velocity with respect to time:

x = ∫ v dt

x = ∫ (t − ∛t) dt

x = ½ t² − ¾ t^(⁴/₃) + C

At time t = 0, x = -4.

-4 = ½ (0)² − ¾ (0)^(⁴/₃) + C

-4 = C

So the position equation is:

x = ½ t² − ¾ t^(⁴/₃) − 4

At time t = 8:

x = ½ (8)² − ¾ (8)^(⁴/₃) − 4

x = 32 − 12 − 4

x = 16

The particle is 16 units to the right of the origin.

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