for beginners or class 11 people...
easy for ones knowing calculus...
a particle is moving with constant speed in the x-y plane...
the trajectory is given by the path is
y=ax3+bx2+cx+d
find the point of time when acceleration is zero...
*EDITS:
1) yeah... take the constant speed to be v!!
2) take the motion starts from the origin...
11well it would be those points for which the double differentiation with respect to t will be
zero, i.e, d2x/dt2 = 0
So the answer to the question
the trajectory is given by the path is
y=ax3+bx2+cx+d
find the point of time when acceleration is zero... is
the point c and d,
Hope am correct :)
71I'm really Confused.
1. Y(x) is given. How are they related to time.
2. @ x=0 , y=d. So how does the particle starts from Origin (0,0)
well it would be those points for which the double differentiation with respect to t will be
zero, i.e, d2x/dt2 = 0
Correct, But Elaborate the Process how you reached there. I don't agree with your answer though!
11Ohh!! I am sorry I made a mistake, but now I don't know how to go about it. :(
Subhomoy you help, Please!
Would it be d2y/dt2 = 0, I am too confused now.
11am attempting once more,
dy/dt =d(y=ax3+bx2+cx+d)/dt
y' =3ax2+2bx + c + 0 (since differentiation of the constant term is zero)
Now, differentiating y' w.r.t t
dy'/dt =d(3ax2+2bx + c)/dt
y" =6ax + 2b
Therefore, d2y/dt2 =6ax + 2b
So the points which have acceleration zero are c and d
11Differentiation of
xn = nxn-1, I made mistake in this differentiation I guess
49well....the equation given gives the trajectory of the particle....
speed is constant throughout....
thus velocity will be constant (i.e. acceleration is zero) when the path is straight
i.e. slope is constant!!!
11Ohhhhhh!!!!!! I just didn't read that. I only saw the equation and started making mistakes.
Thanks Subho :)
From next time I'll read the whole question and then attempt it :)
71dy'/dt =d(3ax2+2bx + c)/dt
Well You cannot differentiate x w.r.t t. Because 'x' is abscissa and NOT the displacement that you can differentiate w.r.t t.
Subho, I thought exactly that BUT I thought you're never wrong. So I started thinking in other way. Really, I need to build up confidence because I solve 90% problems correct but don't know whether I have solved them correctly?!!
Feeling Better as for Now!