The position of a particle moving in the x-y plane at any time t is given by x = (3t^2 - 6t) metres; y = (t^2 - 2t)
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X = 3 t² - 6 t meters y = t² - 2 t m
x = 3 t (t - 2) m y = t (t - 2) m
x = 3 y
Angle made by displacement with x axis = Tan⁻¹ (1/3)
v_x = 6 t - 6 m/s v_y = 2 t - 2 m/s
v_x = 3 v_y
Angle made by velocity with x axis : Tan⁻¹ (1/3)
a_x = 6 m/s^2 a_y = 2 m/s^2
a_x = 3 a_y
angle made by acceleration with x axis = Tan⁻¹ 1/3
a (x,y) = √(36+4) = 2√10 m/sec^2 acceleration is never zero.
v (x,y,t) = √(v²_x +v²_y) = √10 v_y = 2 √10 (t - 1) m/s
velocity is zero at t = 1 sec...
v(t=2 sec) = 2√10 m/s
At t = 2sec, the velocity and acceleration vectors are parallel., as angles made by them with x axis are same
x = 3 t (t - 2) m y = t (t - 2) m
x = 3 y
Angle made by displacement with x axis = Tan⁻¹ (1/3)
v_x = 6 t - 6 m/s v_y = 2 t - 2 m/s
v_x = 3 v_y
Angle made by velocity with x axis : Tan⁻¹ (1/3)
a_x = 6 m/s^2 a_y = 2 m/s^2
a_x = 3 a_y
angle made by acceleration with x axis = Tan⁻¹ 1/3
a (x,y) = √(36+4) = 2√10 m/sec^2 acceleration is never zero.
v (x,y,t) = √(v²_x +v²_y) = √10 v_y = 2 √10 (t - 1) m/s
velocity is zero at t = 1 sec...
v(t=2 sec) = 2√10 m/s
At t = 2sec, the velocity and acceleration vectors are parallel., as angles made by them with x axis are same
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