The position of a particle is given byr-3-0t-i-2-0t2-j-4-0-kmwhere t is in seconds and the coefficients have the proper r to be in metres-a- Find the and a of the particle-b- What is the magnitude and direction of velocity of the particle t - 2-0 s -

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Toppr Admin · Accepted Answer

-a-xA0-x2192-v-t-d-x2192-r-dt-xA0- -xA0- -xA0- -xA0- -3-0-i-x2212-4-0t-j-x2192-a-t-d-x2192-v-t-dt-xA0- -xA0- -xA0- -xA0- -x2212-4-0-j-b-xA0-x2192-v-2-3-0-i-x2212-8-0-jv-2-8-54m-s-x2220-v-2-tan-x2212-1-x2212-8-3-x2212-69-44-x2218-with-xA0-x-xA0-axis

The position of a particle is given by $r = 3.0 t^i - 2.0 t^{2}^j + 4.0^k m$ where t is in seconds and the coefficients have the proper units for $r$ to be in metres(a) Find the $v$ and $a$ of the particle?(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s ?

(a)
$\to v (t) = d \to r / d t$
$= 3.0^i - 4.0 t^j$

$\to a (t) = d \to v (t) / d t$
$= - 4.0^j$

(b)
$\to v (2) = 3.0^i - 8.0^j$
$v (2) = 8.54 m / s$
$∠ v (2) = t a n^{- 1} (- 8 / 3) = - {69.44}^{\circ} w i t h x a x i s$

The position of a particle is given byr=3.0t^i−2.0t2^j+4.0^kmwhere t is in seconds and the coefficients have the proper units for r to be in metres(a) Find the v and a of the particle?(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s ?

(a) →v(t)=d→r/dt =3.0^i−4.0t^j→a(t)=d→v(t)/dt =−4.0^j(b) →v(2)=3.0^i−8.0^jv(2)=8.54m/s∠v(2)=tan−1(−8/3)=−69.44∘with x axis

The position of a particle is given by $r = 3.0 t^i - 2.0 t^{2}^j + 4.0^k m$ where t is in seconds and the coefficients have the proper units for $r$ to be in metres(a) Find the $v$ and $a$ of the particle?(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s ?

(a)
$\to v (t) = d \to r / d t$
$= 3.0^i - 4.0 t^j$

$\to a (t) = d \to v (t) / d t$
$= - 4.0^j$

(b)
$\to v (2) = 3.0^i - 8.0^j$
$v (2) = 8.54 m / s$
$∠ v (2) = t a n^{- 1} (- 8 / 3) = - {69.44}^{\circ} w i t h x a x i s$