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Chapter 9: Q. 22 (page 228)

A $2.0$ kg particle moving along the $x -$ axis experiences the force shown in FIGURE. The particle鈥檚 velocity is $4.0$ m/s at $x = 0$ m. What is its velocity at $x = 2$ m and $x = 4$ m?

Short Answer

Expert verified

Particle's speed at x=2 is 5.10 m/s and at x=4 is 4 m/s

Step by step solution

01

Step 1. Given information

We have,

The mass $m = 2.0$

Particle velocity $4.0$ m/s at $x = 0$ m

02

Step 2. Find the particle speed

The work-kinetic theory gives

$W = K_{f i n a l} - K_{i n i t i a l} K_{f i n a l} = W + K_{i n i t i a l}$

Now,

$\frac{1}{2} m {v^{2}}_{f i n a l} = W + 16 J v_{f i n a l} = \sqrt{\frac{2}{m} (W + 11)} = \sqrt{1 k g^{- 1} 路 (W + 16 J)} x = 2 鈬� W = 10 N 路 2 m 路 \frac{1}{2} = 10 J$

Then, for x=2

role="math" localid="1648175674896" $v_{f i n a l, x = 2} = \sqrt{1 k g^{- 1} 路 (10 J + 16 J)} v_{f i n a l, x = 2} = 5.10 m / s x = 4 鈬� W = 10 N 路 2 m 路 \frac{1}{2} + (- 10 N) 路 2 m 路 \frac{1}{2} = 0 J$

Now, for x=4

$v_{f i n a l, x = 4} = \sqrt{1 k g^{- 1} 路 (0 J + 16 J)} v_{f i n a l, x = 4} = 4 m / s$

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