The velocity of a body of mass 2 , kg as a fu | vedclass

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

Question

(A) Given mass $m = 2 \, kg$ and velocity $\vec{v}(t) = 2t \hat{i} + t^2 \hat{j}$.At $t = 2 \, s$,the velocity is:$\vec{v}(2) = 2(2) \hat{i} + (2)^2 \

Vedclass · Accepted Answer

Momentum = $(8 \hat{i} + 8 \hat{j}) \, kg \cdot m/s$,Force = $(4 \hat{i} + 8 \hat{j}) \, N$

Vedclass · Answer

(A) Given mass $m = 2 \, kg$ and velocity $\vec{v}(t) = 2t \hat{i} + t^2 \hat{j}$.At $t = 2 \, s$,the velocity is:$\vec{v}(2) = 2(2) \hat{i} + (2)^2 \hat{j} = 4 \hat{i} + 4 \hat{j} \, m/s$.Momentum $\vec{p} = m\vec{v} = 2(4 \hat{i} + 4 \hat{j}) = (8 \hat{i} + 8 \hat{j}) \, kg \cdot m/s$.Acceleration $\vec{a} = \frac{d\vec{v}}{dt} = \frac{d}{dt}(2t \hat{i} + t^2 \hat{j}) = 2 \hat{i} + 2t \hat{j}$.At $t = 2 \, s$,acceleration is:$\vec{a}(2) = 2 \hat{i} + 2(2) \hat{j} = 2 \hat{i} + 4 \hat{j} \, m/s^2$.Force $\vec{F} = m\vec{a} = 2(2 \hat{i} + 4 \hat{j}) = (4 \hat{i} + 8 \hat{j}) \, N$.

The velocity of a body of mass $2 \, kg$ as a function of $t$ is given by $\vec{v}(t) = 2t \hat{i} + t^2 \hat{j}$. Find the momentum and the force acting on it at time $t = 2 \, s$.

Similar Questions

The force required to stop a body of mass $10 \,kg$ moving along a straight line path with a velocity of $10 \,ms^{-1}$ in a time of $10 \,s$ is (in $\,N$)

State and explain Newton's second law of motion. Write its important points.

$A$ body,under the action of a force $\vec F = 6\hat i - 8\hat j + 10\hat k$,acquires an acceleration of $1\, m/s^2$. The mass of this body must be

$A$ force on an object of mass $100\, g$ is $(10 \hat{i}+5 \hat{j})\ N$. The position of that object at $t= 2\ s$ is $(a \hat{i}+b \hat{j})\, m$ after starting from rest. The value of $\frac{a}{b}$ will be..........

$A$ particle of mass $m$ is moving in a straight line with momentum $p$. Starting at time $t = 0$,a force $F = kt$ acts in the same direction on the moving particle during time interval $T$ so that its momentum changes from $p$ to $3p$. Here $k$ is a constant. The value of $T$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module