Question

A funny car with mass of m accelerates from rest through a measured track distance with the engine operating at a constant power P. If the track crew can increase the engine power by a differential amount dp, what is the change in the time required for the run? Express your answer exactly in terms of the variables given. dT = Click here to enter or edit your answer dp - T 3P

Answer 1

Answer Giveni T » Time to travel a distance P -) The power of car engine dP >. Power adds by the track to engine- Let the track distance be d' and also let the change time for this increase in power. de to be de. in : Power, P = dw ( Rate of change of work) dt According to worka energy theorem KE my? À 2 :. d dt Emv): -- d(3) dt. 2 2vdu my dy dt dt 2 dt mv 뜹 dv 0 Р

Integrating at too; V;0 and tot op, VEVO dt = mv dv. Р 0 0 2 T ma ap Now we COLD write; da w vdt Substitute © in dv. V. mv P s dx mye dri d NE da mv² dv P O mV ЭР 2 da MVT Squaring a 3P Multiply by 8 mp 80P 6 d² 8m PVT m² vit EP am 8.9 mp3 d² 8P T = mv mate ЗР am 9 mnd' PT3 C. (c is a constant) Differentiating the equation with respect to p. 43 dp + 3 pt dt = 0 => T3 d P = -3pridr. Tdp = d7 = 3 P: