Question

Consider the following position function. Find (a) the velocity and the speed of the object and (b) the acceleration of the object r(t) = (3t 6,6t - 5,2 + 3t) for t greater than equal to 0. a. What is the velocity of the object? v(t) = What is the speed of the object? |v(t)| = b. What is the acceleration of the object? a(t) =

Answer 1

Answer:

Step-by-step explanation:

Given that the position vector of a moving body at time t is

$r(t) = (3t ^6,6t - 5,2 + 3t), t\geq 0$

Velocity is the derivative of acceleration

v(t) = $(18t^5, 6, 3)$, t positive

Speed would be the magnitude of the velocity and will not have direction

Speed = $\sqrt{324t^{10}+36+9 } \\=\sqrt{324t^{10}+45)$

Acceleration of the object

a(t) = derivative of velocity of vector

= $(90t^4, 0,0)$

i.e. acceleration would be in the direction of x axis alone.