00:01
Hello, let's have a look on the question.
00:02
So it is given to us that rt is equal to minus 3t, minus 2t square and minus 3t cube.
00:12
At t is equal to 2.
00:14
We need to find out at and an.
00:17
So the formula for at is r -d -t into r -dabble -t, this is dot product, divided by magnitude of r -d -t.
00:26
And formula for an is equal to r -d -t.
00:32
Product of r -dash t and r double dash t divided by magnitude of r -dash t so for the first part we will find out at so value of r -dash t is equal to minus three minus four t and minus nine t square the value for r double dash t will be equal to this will be zero and this is minus four and minus 18 t so now we will find out the magnitude of r -dash t so this will be equal to under root of minus 3 whole square minus 4 t whole square plus 90 square whole square negative of 90 square whole square so this value will be equal to 9 plus 16 t square at 1 t to the power 4 now to find a n we need these 3 values.
01:33
So, for finding a .t.
01:36
So for the force part, 80 is equal to dot product, that is minus 3, minus 4 t, minus 9 t squared, dot product, 0 minus 4 minus 18 t, divided by under root of 9 plus 16 t squared plus 81 t to the power 4.
01:59
So when we will multiply, these values will be 3 into 0 as this will be 0.
02:05
This will be positive 16 t plus 162 t to the power 3 divided by under root of 9 plus 16 t square plus 81 t to the power 4 or we can write it as this is 8 t of t is equal to 16 t plus 162 t q divided by under root of 9 plus 16 t square plus 81 t to the power 4 now we have the value of t2 so we can put 2 at the place of t so these values will become this will be 16 into 2 plus 162 into 2 whole cube divided by 9 plus 16 into 2 square plus 81 into 2 to the power 4 so this will be equal to 32 plus 1 ,296 divided by under root of 9 plus 64 plus 1296.
03:12
So this value is equal to 1328 divided by under root of 1369.
03:20
And this value is 37...