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# Find the velocity, acceleration, and speed of a particle with position function

Find the velocity, acceleration, and speed of a particle with position function r(t) = <-7tsin(t), -7tcos(t), 4t^2>

v(t) = <?, ?, ?>
a(t) = <?, ?, ?>
|v(t)|= ?

### 2 Answers by Expert Tutors

Dr Gulshan S. | Experienced Physics Tutor with a PhDExperienced Physics Tutor with a PhD
4.8 4.8 (5 lesson ratings) (5)
2
Hi Ally

V = derivative of r wrt time

V = dr/dt
V= d/dt(-7tsint) = -7t. cos t -7sint
and acceleration  is derivative of velocity  wrt time

dV/dt =d/dt ( -7t.cost -7sint) or second derivative of position

= 7t sint -7cost - 7 cost
= 7t sint -14 cost
Similarly for other two functions
Arturo O. | Experienced Physics Teacher for Physics TutoringExperienced Physics Teacher for Physics ...
5.0 5.0 (66 lesson ratings) (66)
0
Ally,

When a vector is given in terms of the CONSTANT unit vectors ij, and k, as in this problem, all you have to do is differentiate each component.

r = <x(t), y(t), z(t)>

v = <dx/dt, dy/dt, dz/dt>

a = <d2x/dt2, d2y/dt2, d2z/dt2>

v = |v| = √[(dx/dt)2 + (dy/dt)2 + (dz/dt)2]

Thanks
I thought there are three different values of r as it was not in i , j , k form
Good you pointed out