Resuelve el siguiente ejercicio de velocidad. El vector de posición de un móvil es r (t) =2 (t −7) i +12t j, en intervalos de tiempo t1 = 5 s y t2 =8s en unidades SI. Determina: Su velocidad.

To Find :

Position vector at time and .

Solution :

r (t) = 2 (t −7)i + 12t j

Putting t = 5 s and t = 8 s, we get :

r(5) = 2( -2 )i + 60j

r(5) = -4i + 60j

r(8) = 2i + 96j

Now, to find speed differentiating the r(t) w.r.t t :

Hence, this is the required solution.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is