A body of 0.5 ~kg moves along the positive x -axis under the influence of a varying force F (in Newtons) as shown below. If the speed of the object at x=4 ~m in 3.16 ~ms^ -1 then its speed at x=8 ~m is

Correct answer: D. 6.8 ~ms^ -1 According to work-energy principle array l W_ C +W_ nc +W_ ext =Δ KE ∫_ 4 ^ 8 Fdx=(1)/(2) mv_ f ^ 2 -(1)/(2) mv_ i ^ 2 array (1)/(2) × 3 × 8-(1)/(2) × 1.5 × 4=(1)/(2) × (1)/(2) [v_ f ^ 2 -(3.16)^ 2 ] v_ f =6.8 ~m / s

NEET

Exam: NEET
Subject: Physics
Chapter: Motion in One Dimension

NEET · Physics · Motion in One Dimension

A body of 0.5 ~kg moves along the positive x -axis under the...

A body of

0.5 \mathrm{~kg}

moves along the positive

\mathrm{x}

-axis under the influence of a varying force

\mathrm{F}

(in Newtons) as shown below. A body of 0.5 ~kg moves along the positive x -axis under the influence of a varying force F (in Newtons) as shown

If the speed of the object at

x=4 \mathrm{~m}

3.16 \mathrm{~ms}^{-1}

then its speed at

x=8 \mathrm{~m}

Options

A $3.16 \mathrm{~ms}^{-1}$
B $9.3 \mathrm{~ms}^{-1}$
C $8 \mathrm{~ms}^{-1}$
D $6.8 \mathrm{~ms}^{-1}$

Correct answer

D. $6.8 \mathrm{~ms}^{-1}$

Step-by-step solution

According to work-energy principle

\begin{array}{l} \mathrm{W}_{\mathrm{C}}+\mathrm{W}_{\mathrm{nc}}+\mathrm{W}_{\mathrm{ext}}=\Delta \mathrm{KE} \\ \int_{4}^{8} \mathrm{Fdx}=\frac{1}{2} \mathrm{mv}_{\mathrm{f}}^{2}-\frac{1}{2} \mathrm{mv}_{\mathrm{i}}^{2} \end{array}

\frac{1}{2} \times 3 \times 8-\frac{1}{2} \times 1.5 \times 4=\frac{1}{2} \times \frac{1}{2}

\left[v_{f}^{2}-(3.16)^{2}\right] v_{f}=6.8 \mathrm{~m} / \mathrm{s}

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