At time t=0 a particle starts travelling from a height 7 hat z cm in a plane keeping z coordinate constant. At any instant of time it's position along the hat x and hat y directions are defined as 3 t and 5 t 3 respectively. At t =1 s acceleration of the particle will be

Question

At time t=0 a particle starts travelling from a height 7 hat z cm in a plane keeping z coordinate constant. At any instant of time it's position along the hat x and hat y directions are defined as 3 t and 5 t 3 respectively. At t =1 s acceleration of the particle will be (A) -30 haty (B) 30 haty (C) 3 hatx+15 haty (D) 3 hat x +15 hat y +7 hat z

Tardigrade Admin · Accepted Answer

r =3 hat t +5 t 3 hat j +7 k ( d 2 r / dt 2)=30 t hat j At t =1 ⇒ ( d 2 r / dt 2)=30 hat j

$- 30 \overset{y}{^}$

$30 \overset{y}{^}$

$3 \overset{x}{^} + 15 \overset{y}{^}$

$3 \overset{x}{^} + 15 \overset{y}{^} + 7 \overset{z}{^}$

$r = 3 \hat{t} + 5 t^{3} \hat{j} + 7 k$
$\frac{d ^{2} r}{d t ^{2}} = 30 t \hat{j}$
At $t = 1 \Rightarrow \frac{d ^{2} r}{d t ^{2}} = 30 \hat{j}$

Q. At time t=0 a particle starts travelling from a height 7z^cm in a plane keeping z coordinate constant. At any instant of time it's position along the x^ and y^​ directions are defined as 3t and 5t3 respectively. At t=1s acceleration of the particle will be

−30y^​

30y^​

3x^+15y^​

3x^+15y^​+7z^

r=3t^+5t3j^​+7k dt2d2r​=30tj^​ At t=1⇒dt2d2r​=30j^​

$- 30 \overset{y}{^}$

$30 \overset{y}{^}$

$3 \overset{x}{^} + 15 \overset{y}{^}$

$3 \overset{x}{^} + 15 \overset{y}{^} + 7 \overset{z}{^}$

$r = 3 \hat{t} + 5 t^{3} \hat{j} + 7 k$
$\frac{d ^{2} r}{d t ^{2}} = 30 t \hat{j}$
At $t = 1 \Rightarrow \frac{d ^{2} r}{d t ^{2}} = 30 \hat{j}$