Douglas has finished alterations on his BMW Isetta and challenges Martin, drivin

Question

Douglas has finished alterations on his BMW Isetta and challenges Martin, driving a custom Reliant Robin, to a street race. The Robin, of mass m, accelerates from rest using the engine’s maximum power output P, which remains constant during the acceleration. The Isetta accelerates from rest at a constant rate a. (a) To what speed does the Robin accelerate when it has traveled a distance x from its starting position? (b) Express x in terms of the time t during which this distance is covered. (c) Calculate the ratio (leading to trailing) of the cars’ displacements (from the starting line) at the instant when the trailing car begins to close in on the leading car. (d) Determine the ratio (fast to slow) of the cars’ speeds when the trailing car passes the leading one. (e) What time elapses between the two events described in (c) and (d)? note: given answers are ; (a) 3px/m, (b) 8pt^3/pm (c) 4/3 (d) 4/3 (e) 14p/9ma^2. please show work in details.

Explanation / Answer

a)

Robin with mass -m,

Acceleration - a,

using the equation of motion

v2= u2 + 2ax [ a =F/m ; P = Fv;]

v = 3px/m

(b) x = ut + 1/2at2 [ p = fx/t]

= 8pt^3/pm

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