The equation of motion of a particle moving along a straight line is , where the units of and are cm and sec. The acceleration of the particle will be zero
Step 1: Given data:
Equation of motion,
Let at the acceleration of the particle will be zero.
Step 2: Formula used:
The relation between acceleration and displacement is given by-
Where is acceleration, is a displacement.
Step 3: Calculation of time
The given equation of motion is-
Using the formula, the acceleration can be calculated as
Differentiate the equation of motion in equation (1) with respect to time.
Again differentiating the equation (2) with respect to time.
We know that from the relation between acceleration and displacement that
Equating the equation (3) and equation (4)
But it is given that the acceleration of the particle will be zero at time
Substituting the known values that the acceleration for finding time.
Hence, option A is the correct answer.