00:01
In this problem, we have been given the equation of a motion of the particle provided that the x is measured in meters and t is measured in seconds.
00:10
So we need to determine the time when the velocity of the object is zero.
00:15
So velocity, as we know, that's described as the rate of change of position.
00:19
So we differentiate this equation of x as a function of t with respect to time.
00:24
So we get 6t square minus 30 t plus 24 upon differentiating.
00:29
And this is given out to be zero.
00:32
So we just solve this quadratic equation and we get two values of time and that's one second and four seconds.
00:40
So at both these times, the object is having zero velocity.
00:44
And now we have to figure out the time when the acceleration of this particle is zero.
00:50
So first to do that, we differentiate velocity with respect to time and that gets us 12 -t minus 30.
00:57
And this is given out to be zero...