Answered: "The acceleration of a particle is defined by..."

High School
Physics
Force, Motion and Energy
Acceleration Due to Gravity

iamerkviladzekiu

Answered question

2023-02-12

The acceleration of a particle is defined by the relation,

a = - 4 x (- 1 + \frac{1}{4} x^{2})

, where x is displacement along x-axis. All the quantities are in SI units. If velocity of the particle (v)=17 m/s when x=0, then the velocity of the particle when x=4 m is
A) 12 m/s
B) 15 m/s
C) 20 m/s
D) 25 m/s

Answer & Explanation

Zaria House

Beginner2023-02-13Added 2 answers

The correct answer is B 15 m/s
Given,

a = - 4 x (- 1 + \frac{1}{4} x^{2}) = v \frac{d v}{d x}

\Rightarrow \int_{17}^{v} v d v = \int_{0}^{4} (4 x - x^{3}) d x

\Rightarrow \frac{1}{2} [v^{2}]_{17}^{v} = \frac{4}{2} [x^{2}]_{0}^{4} - \frac{1}{4} [x^{4}]_{0}^{4}

\Rightarrow v^{2} - 17^{2} = 4 (4^{2} - 0) - \frac{1}{2} (4^{4} - 0)

\Rightarrow v^{2} = 225

⇒v=15 m/s

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