Respuesta :
To Find :
Position vector at time [tex]t_1 = 5\ s[/tex] and [tex]t_2 = 8\ s[/tex].
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 :
[tex]v=\dfrac{dr}{dt}= \dfrac{d(2(t-7)i + 12tj)}{dt}\\\\v=\dfrac{dr}{dt}= 2i + 12j[/tex]
Hence, this is the required solution.
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,
[tex]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 \\\\[/tex]
v(t)=2i +12j
Hence, the velocity vector, v(t)=2i +12j.
