00:01
The displacement equation is x equal to 20 t minus 5 t squared.
00:12
Then the velocity expression will be d x by d t.
00:17
It means d by d t of expression for x is 20 t minus 5 t squared.
00:28
If we solve it further, then it is b by d t of 20 t minus 5 t.
00:39
D by d t of 5 t square 20 is constant outside and d t by d t is 1 so it is 20 minus here 5 is constant and d t of t square is 2 t so expression for means velocity becomes 20 minus 10 t now about acceleration acceleration is equal to d b b by d t it means d by d t of the velocity is 20 minus 10 t right so this is d t by d by d by d t of constant 20 minus d by d t of 10 t now d by d t of constant is 0 minus 10 is outside and d t by d t is 1 so it is minus 10 so acceleration is equal to minus 10 meter per second square velocity is meter per second and this is meter.
01:55
So we have expression for all these three.
02:00
Now in part a, they are asking when if ever the particle velocity is zero.
02:07
Okay, so it means v is equal to zero means the expression for velocity is 20 minus 10 is zero.
02:17
This gives us 20 is equal to 10.
02:22
Means t is equal to two seconds.
02:26
So the particle velocity is zero at t equal to two seconds.
02:32
Part b, they are asking when acceleration is zero.
02:35
Now the acceleration is always minus 10 meter per second square.
02:41
Its expression does not contain time.
02:43
So acceleration is constant and it is always minus 10 meter per second square.
02:49
And it is never zero.
02:54
Part c, x is acceleration, when acceleration is negative, when it is positive.
03:07
So acceleration is always negative.
03:12
Acceleration is always negative.
03:22
It is never positive.
03:27
It is never positive...