Hello Everyone, please help me on this dynamics questions!
A particle has an initial velocity U and after travelling a distance d in time T along a straight path its velocity is V. The retardation of the particle is proportional to its velocty at any time. Show that:
U = V e ^ ( T(U-V)/d )
Acceleration = .
The first part of this problem connects velocity, time, and acceleration, so we express the phrase:in the formThe retardation of the particle is proportional to its velocty at any time
where is a positive constant
, noting that the boundary conditions have been incorporated into the limits of the integrals.
Next we use the alternative expression for acceleration, in order to relate velocity, acceleration and distance:
, where is a positive constant.
, noting again the boundary conditions as limits.
From here we can find another expression for , in terms of V, U and d (it's very easy!). And hence, from equation (1), we can get the result.
Can you complete it now?