The equation of motion of a particle starting from rest along a straight line is x = t3 – 3t2 + 5. The ratio of the accelerations after 5 sec and 3 sec will be A. 2 B. 3 C. 4 D. 5

The correct answer is $\boxed{\text{C}}$.

The acceleration of a particle is given by $a = \frac{d^2x}{dt^2}$. In this case, we have $x = t^3 – 3t^2 + 5$, so $a = 3t^2 – 6t$.

The acceleration after 5 seconds is $a(5) = 3(5)^2 – 6(5) = 15$.

The acceleration after 3 seconds is $a(3) = 3(3)^2 – 6(3) = 9$.

The ratio of the accelerations is $\frac{a(5)}{a(3)} = \frac{15}{9} = \boxed{5}$.

Here is a brief explanation of each option:

• Option A: $2$. This is the
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