Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...

Engineering Mathematics - II - Vector Calculus - 2007
t
d r / dt
ds / dt
d t/ dt
| d r / dt |
1
( 3 cos t i 3 sin t j)
25
unit normal vector
d t/ ds
N
| d t/ ds |
3
(cos t i sin t j)
25
3 / 25
(cos t i sin t j)
14. The position vectors of a moving particle at time t is r t
2
i t
3
j
t
4
k .
Find the tangential and normal components of its acceleration at t = 1.
Suggested answer:
r t
2
i
t
3
j
t
4
k
v
d r
dt
2t i 3t
2
j
4t
4
k
v t1
2 i 3 j
4 k
v
1
(2 i 3 j
4 k)
29
a t1
2 i 6 j
12 k
Page 47 of 72