SOLUTION: The x- and y-coordinates of moving particle are given by the parametric equation x = 5tē + t and y = 2-8t. Find the magnitude of velocity at t = 3 seconds. The distance is

Algebra ->  Test -> SOLUTION: The x- and y-coordinates of moving particle are given by the parametric equation x = 5tē + t and y = 2-8t. Find the magnitude of velocity at t = 3 seconds. The distance is       Log On


   

Question 1114631: The x- and y-coordinates of moving particle are given by the parametric equation
x = 5tē + t and y = 2-8t.
Find the magnitude of velocity at t = 3 seconds. The distance is measured in meters.
* curvilinear motion
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28v%29=sqrt%28%28dx%2Fdt%29%5E2%2B%28dy%2Fdt%29%5E2%29
dx%2Fdt=10t%2B1
dy%2Fdt=-8
When t=3,
dx%2Fdt=10%283%29%2B1=30%2B1=31
dy%2Fdt=-8
So,
abs%28v%29=sqrt%28%2831%29%5E2%2B%28-8%29%5E2%29
Work that out for the answer.

Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.
Calculate x- and y-components of the velocity vector  V%5Bx%5D = %28dx%29%2F%28dt%29  and  V%5By%5D = %28dy%29%2F%28dt%29  at t= 3 seconds.


Then the magnitude of velocity is  |V| = sqrt%28%28%28dx%29%2F%28dt%29%29%5E2+%2B+%28%28dy%29%2F%28dt%29%29%5E2%29.