A body of mass 1 , kg starts moving from rest | vedclass

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

Question

(B) Given $K.E. = \frac{1}{2}mv^2 = 2t^2$. Since $m = 1 \, kg$,we have $\frac{1}{2}(1)v^2 = 2t^2$,which implies $v^2 = 4t^2$,so $v = 2t \, m/s$.Tangen

Vedclass · Accepted Answer

power of all forces at $t = 2 \, s$ is $8 \, W$

Vedclass · Answer

(B) Given $K.E. = \frac{1}{2}mv^2 = 2t^2$. Since $m = 1 \, kg$,we have $\frac{1}{2}(1)v^2 = 2t^2$,which implies $v^2 = 4t^2$,so $v = 2t \, m/s$.Tangential acceleration $a_t = \frac{dv}{dt} = \frac{d}{dt}(2t) = 2 \, m/s^2$. Thus,option $A$ is incorrect.Power $P = \frac{d(K.E.)}{dt} = \frac{d}{dt}(2t^2) = 4t$. At $t = 2 \, s$,$P = 4(2) = 8 \, W$. Thus,option $B$ is correct.Tangential force $F_t = m \cdot a_t = 1 \cdot 2 = 2 \, N$. Thus,option $D$ is incorrect.For the first round,distance $s = 2\pi r = 2\pi(8) = 16\pi \, m$. Since $v = 2t$,$s = \int v \, dt = \int_0^T 2t \, dt = T^2$. Setting $T^2 = 16\pi$,$T = 4\sqrt{\pi} \, s 
eq 2 \, s$. Thus,option $C$ is incorrect.

$A$ body of mass $1 \, kg$ starts moving from rest at $t = 0$ in a circular path of radius $8 \, m$. Its kinetic energy varies as a function of time as: $K.E. = 2t^2 \, J$,where $t$ is in seconds. Then:

Similar Questions

Two particles of equal masses are revolving in circular paths of radii $r_1$ and $r_2$ respectively with the same speed. The ratio of their centripetal forces is

$A$ car starts from rest and accelerates at $5 \, m/s^{2}$. At $t=4 \, s$,a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t=6 \, s$? (Take $g = 10 \, m/s^{2}$)

$A$ block of mass $5 \, kg$ is moving with a horizontal velocity of $1.5 \, m/s$. $A$ force of $5 \, N$ is applied in the perpendicular (vertical) direction for $4 \, s$. The total distance covered by the block is .......... $m$.

What determines the nature of the path followed by a particle?

$A$ plane is revolving around the Earth with a speed of $100\, km/hr$ at a constant height from the surface of the Earth. The change in the velocity as it travels a half circle is ......... $km/hr$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module