Motion in a Plane

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Question : 23
Total: 32
For any arbitrary motion in space, which of the following relations are true :
(a)
v
average
=(
1
2
)
[
v
(t1)
+
v
(t2)
]

(b)
v
average
=
[
r
(t2)
r
(t1)
]
(t2t1)

(c)
v
(t)
=
v
(0)
+
a
t

(d)
r
(t)
=
r
(0)
+
v
(0)
t
+(
1
2
)
a
t2

(e)
a
average
=
[
v
(t2)
v
(t1)
]
(t2t1)

The ‘average’ stands for average of the quantity over the time interval t1tot2
Solution:  
Relations (b) and (e) are true for any arbitrary motion in space.
Relations (a), (c) and (d) are false as they hold for uniformly accelerated motion. For arbitrary motion, acceleration is not uniform.
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