A body of mass 2 , kg moves under a force of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given: mass $m = 2 \, kg$,force $\vec{F} = (2 \hat{i} + 3 \hat{j} + 5 \hat{k}) \, N$,initial velocity $\vec{u} = 0$,initial position $\vec{r}_0 =

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(C) Given: mass $m = 2 \, kg$,force $\vec{F} = (2 \hat{i} + 3 \hat{j} + 5 \hat{k}) \, N$,initial velocity $\vec{u} = 0$,initial position $\vec{r}_0 = (0, 0, 0)$,time $t = 4 \, s$.Using Newton's second law,the acceleration $\vec{a}$ is:$\vec{a} = \frac{\vec{F}}{m} = \frac{2 \hat{i} + 3 \hat{j} + 5 \hat{k}}{2} = \hat{i} + 1.5 \hat{j} + 2.5 \hat{k} \, m/s^2$.Using the kinematic equation for position $\vec{r} = \vec{r}_0 + \vec{u}t + \frac{1}{2} \vec{a} t^2$:$\vec{r} = 0 + 0 + \frac{1}{2} (\hat{i} + 1.5 \hat{j} + 2.5 \hat{k}) (4)^2$$\vec{r} = \frac{1}{2} (\hat{i} + 1.5 \hat{j} + 2.5 \hat{k}) (16)$$\vec{r} = 8 \hat{i} + 12 \hat{j} + 20 \hat{k}$.Comparing this with the given coordinates $(8, b, 20)$,we find $b = 12$.

$A$ body of mass $2 \, kg$ moves under a force of $(2 \hat{i} + 3 \hat{j} + 5 \hat{k}) \, N$. It starts from rest and was at the origin initially. After $4 \, s$,its new coordinates are $(8, b, 20)$. The value of $b$ is ........ . (Round off to the Nearest Integer)

Similar Questions

If a ship of mass $4 \times 10^{7} \,kg$ initially at rest is pulled by a force of $5 \times 10^{4} \,N$ through a distance of $4 \,m$, then the speed of the ship will be (resistance due to water is negligible). (in $\,ms^{-1}$)

What is the minimum acceleration with which a person can slide down a rope,if the breaking strength of the rope is $\frac{2}{3}$ of the person's weight?

$A$ block $P$ of mass $M_P$ is in contact with another block $Q$ of mass $M_Q$ as shown in the figure and they are placed on a smooth floor. Find the force on block $Q$.

$A$ monkey of mass $m$ is climbing a rope hanging from the roof with acceleration $a$. The coefficient of static friction between the body of the monkey and the rope is $\mu$. Find the direction and value of the friction force on the monkey.

Three masses of $16 \, kg$,$8 \, kg$,and $4 \, kg$ are placed in contact as shown in the figure. If a force of $140 \, N$ is applied on the $4 \, kg$ mass,then the force on the $16 \, kg$ mass will be ............ $N$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module