a particle starts its motion from origin with velocity 2i cap m/s and moves in xy plane with uniform acceleration 1 icap+ 3j cap a) what will be the value of y coordinate when value of x coordinate is 30m b) what will be its speed at this time??
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ANSWER
U
x
=5
i
^
(m/s)
U
y
=0(m/s)
a
x
=3
i
^
(m/s
2
)
a
y
=2
j
^
(m/s
2
)
(a)
S
x
=
U
x
t+
2
1
a
x
t
2
84
i
^
=5t
i
^
+
2
1
×3×t
2
i
^
∴3t
2
+10t=168
3t
2
+10t−168=0
3t
2
+28t−18t−168=0
t(3t+28)−6(3t
2
+28)=0
(t−6)(3t
2
+28)=0
∵ time can't be negative.
∴t=6
At t=6,
S
x
=84
i
^
(m)
∴
S
y
=0+
2
1
a
y
t
2
j
^
=
2
1
×2×36
j
^
S
y
=36
j
^
∴Y− coordinate at (t−6)⇒36m
(b)
V
x
=
U
x
+
a
x
t
5+3×6
=23i(m/s)
V
y
=0+2×6
j
^
=12
j
^
(m/s)
∣V∣=
23
2
+12
2
25.94m/s$
∣V∣≈26m/s
Where ∣V∣= Speed of particle at t=6)
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