If the distance ‘’ metre traversed by a particle in seconds is given by , then the velocity of the particle when the acceleration is zero, in is,
Step 1: Given data
The distance ‘’ metre traversed by a particle in seconds is,
Step 2: Formula used
The first derivative of displacement is velocity
That is,
Acceleration() is the derivative of velocity with respect to time.
That is,
In other words, acceleration() is the second derivative of displacement().
That is,
Step 3: Find Velocity ():
Velocity() is the rate of change of distance of an object with respect to time.
Here,
Velocity,
That is,
Step 4: Find Acceleration ():
Acceleration() is the rate of change of the velocity of an object with respect to time.
Acceleration,
That is,
Step 5: Find Velocity at :
To find the time t where the acceleration becomes zero, equate the equation (2) to zero
That is,
Substitute this in equation (1)
Therefore, the velocity of the particle when the acceleration is zero, in is .