A particle is projected with velocity 𝑉0 along 𝑥-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e. 𝑎 = 𝛼𝑥 2 , the distance at which the particle stops is

April 19, 2022

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Physics Problems

Question : A particle is projected with velocity 𝑉0 along 𝑥-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e. 𝑎 = 𝛼𝑥 2 , the distance at which the particle stops is

(A) $\sqrt{\dfrac{3V_{0}}{2\alpha }}$

(B) $\left( \dfrac{3V_{0}}{2\alpha }\right) ^{\dfrac{1}{3}}$

(D) $\left( \dfrac{3V_{0}^{2}}{2\alpha }\right) ^{\dfrac{1}{3}}$

Answer : option (D)

Solution :

A particle is projected with velocity 𝑉0 along 𝑥-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e. 𝑎 = 𝛼𝑥 2 , the distance at which the particle stops is