The acceleration 𝑎 of a particle starting from rest varies with time according to relation 𝑎 = 𝛼𝑡 + 𝛽. The velocity of the particle after a time 𝑡 will be

April 10, 2022

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Physics Problems

Question : The acceleration 𝑎 of a particle starting from rest varies with time according to relation 𝑎 = 𝛼𝑡 + 𝛽. The velocity of the particle after a time 𝑡 will be

(A) $\dfrac{at^{2}}{2}\beta$

(B) $\dfrac{at^{2}}{2}\beta t$

(D) $\dfrac{\left( at^{2}+B\right) }{2}$

Answer : option (B)

Solution :

The acceleration 𝑎 of a particle starting from rest varies with time according to relation 𝑎 = 𝛼𝑡 + 𝛽. The velocity of the particle after a time 𝑡 will be