Question

The x- and y- coordinates of moving particle are given by the parametric equation x=4t^2 + t and y = 2-4t.

Find the magnitude of the velocity at t=2 seconds. The distance is measured in meters.


Round your answer to 1 decimal place.

Answer 1

17.5 m/s

Explanation:

The magnitude of velocity is the root of the sum of the squares of the x- andy-velocities.

x' = 8t +1

y' = -4

At t = 2, the respective velocities are ...

x'(2) = 8·2 +1 = 17

y'(2) = -4

Then the velocity is ...

v(2) = √(17^2 +(-4)^2) = √305

v(2) ≈ 17.5 . . . . meters/second