A point has a position vector given by r(t)=(2t,t^2) for all time t ≥ 0 seconds. Find the speed of the object at t = 1 seconds. 8 4 2 2√(2)

Question

A point has a position vector given by
`r(t)=(2t,t^2)` for all time t ≥ 0 seconds. Find the speed of the object at t = 1 seconds.

8
4
2

`2√(2)`

Answer 1

2√2

Explanation:

r(t) = (2t, t²)

v(t) = dr/dt

v(t) = (2, 2t)

v(1) = (2, 2)

|v(1)| = √(2² + 2²)

|v(1)| = 2√2