Question

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.

Answer 1

To Find :

Position vector at time $t_1 = 5\ s$ and $t_2 = 8\ s$.

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 :

$v=\dfrac{dr}{dt}= \dfrac{d(2(t-7)i + 12tj)}{dt}\\\\v=\dfrac{dr}{dt}= 2i + 12j$

Hence, this is the required solution.

Answer 2

Answer:

The velocity vector, v(t)=2i +12j

Step-by-step explanation:

The given position vector,

r (t) = 2 (t −7) i + 12t j

So, the velocity vector,

$v(t)= \frac {d}{dt} r(t) \\\\v(t)= \frac {d}{dt}2(t-7)i+ 12t j \\\\v(t)=\frac {d}{dt} 2(t-7)i + \frac {d}{dt} (12t)j$

v(t)=2i +12j

Hence, the velocity vector, v(t)=2i +12j.