Chapter 9: Q. 22 (page 228)

A $2.0$ kg particle moving along the $x -$ axis experiences the force shown in FIGURE. The particle’s 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

Step 1. Given information

We have,

The mass $m = 2.0$

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

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,

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

Then, for x=2

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

Now, for x=4

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

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the particle speed

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the particle speed

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Famous Physicists

Electrostatics

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Study anywhere. Anytime. Across all devices.

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