Question

Acceleration $\left(a\right)$ versus displacement $\left(x\right)$ and potential energy $\left(U\right)$ versus $x$ of a particle moving along x-axis is shown. Mass of the particle is $1kg$ and it has velocity $4m/s$ at $x=0$

• A. Kinetic energy at $x=4m$ is $88J$
• B. Work done by conservative forces from $x=0$ to $x=8m$ is $240J$
• C. Total work done on particle when it is at $x=8m$ is $120J$
• D. Work done by non-conservative forces from $x=0$ to $x=8m$ is $-120J$

Answer 1

The correct option is A Kinetic energy at $x=4m$ is $88J$

From kinematics:$v^2-u^2=2as$ where

$v$ is final velocity

$u$ is initial velocity=4 m/s

$a$ is acceleration.

$s$ is the displacement.

At $x=4m:v^2=16+2\times 20\times 4=16+160=176$

Kinetic energy $=\frac{1}{2}m{v}^2=\frac{1}{2}\times 1\times 176=88J$

Work done by conservative forces from $x=0$ to $x=8m$ can be calculated from the second graph by subtracting the area BCDE from the area ABC:

Work $=-\frac{1}{2}\times 4\times 120+[\frac{120}{2}\times (4+8\left)\right]=-240+720=480J$

(First is positive and second is negative because of work-energy theorem which says:$\Delta W=k_2-k_1=u_1-u_2$,where k is kinetic energy.)