A particle of mass m kg moves along the X-ax | vedclass

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

Question

(B) According to the work-energy theorem, the total work done by all forces is equal to the change in kinetic energy of the particle.Work done $W = \D

Vedclass · Accepted Answer

$\frac{m k^2}{2} d^{2 \beta}$

Vedclass · Answer

(B) According to the work-energy theorem, the total work done by all forces is equal to the change in kinetic energy of the particle.Work done $W = \Delta KE = KE_f - KE_i$.The velocity of the particle is given by $v = k x^\beta$.At $x = 0$, the initial velocity $v_i = k(0)^\beta = 0$.At $x = d$, the final velocity $v_f = k d^\beta$.The initial kinetic energy $KE_i = \frac{1}{2} m v_i^2 = \frac{1}{2} m (0)^2 = 0$.The final kinetic energy $KE_f = \frac{1}{2} m v_f^2 = \frac{1}{2} m (k d^\beta)^2 = \frac{1}{2} m k^2 d^{2\beta}$.Therefore, the total work done $W = \frac{1}{2} m k^2 d^{2\beta} - 0 = \frac{m k^2}{2} d^{2\beta}$.

$A$ particle of mass $m \ kg$ moves along the $X$-axis with its velocity varying with the distance travelled as $v=k x^\beta$, where $k$ is a positive constant. The total work done by all the forces during displacement of the particle from $x=0$ to $x=d$ is close to

Similar Questions

What can be said about the law of conservation of energy?

$A$ particle of mass $m$ moves with a velocity $v = a\sqrt{x}$,where $a$ is a constant and $x$ is the displacement. Find the total work done by all forces during the displacement from $x = 0$ to $x = d$.

$A$ ball of mass $300 g$ is dropped from a height $10 m$ above a sandy ground. On reaching the ground,it penetrates through a distance $1.5 m$ in sand and finally stops. The average resistance offered by the sand to oppose the motion is (acceleration due to gravity $= 10 m s^{-2}$) (in $N$)

$A$ car driver is trying to jump across a path as shown in the figure by driving horizontally off a cliff '$X$' at a speed of $10 \ m \ s^{-1}$. When he touches peak '$Z$' (ignore air resistance), what would be his speed (in $m \ s^{-1}$)? (use $g = 10 \ m \ s^{-2}$)

Explain the conservation of mechanical energy using the example of a falling ball.

Vedclass Test Series

Exam Paper Generator

Online Exam Module