Q.[Class 11th] A particle moves in the x-y plane and its x and y coordinate depends on time(t) in sec given by x=8t metre and y=6t-t² metre then find its speed at t=0 second and t=2 second. Also derive equation of trajectory.
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Answer:
Given,
x=4t
2
+5t+16
y=5t
velocity along x-axis
v
x
=
dt
dx
=(8t+5)m/s
acceleration along x-axis,
a
x
=
dt
v
x
=8m/s
velocity alon y-axis
v
y
=
dt
dy
=5m/s
acceleration along y- axis,
a
y
=
dt
v
y
=0m/s
The acceleration of the particle is given by
a
=a
x
i
^
+a
y
j
^
∣
a
∣=
a
x
2
+a
y
2
a=
8
2
+0
2
=8m/s
2
Explanation:
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Answer:
A particle moves in an XY-plane in such a way that its x and y-coordinates vary with time according to <br> x(t)=t^(3)-32t, y(t)=5t^(2)+12 <br> Find the acceleration of the particle, if t = 3 s.
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