Two cars are drag racing, starting from rest at t=0, on a straight and level roa

Question

Two cars are drag racing, starting from rest at t=0, on a straight and level road. Team Alpha's car produces acceleration.   Ax=(alpha)t^(-1/2), while Team Beta's car produces acceleration Ax=(Beta), for all t>0, where Alpha and Beta are positive constants with suitable units.

a.) Which car grabs the early lead ? Remember to justify your answer.

b.) If the race goes on long enough , the other car will overtake the early leader. Find an expression for the distance x at which this will occur in terms of the constant (Alpha) and (Beta)

Explanation / Answer

a.) we cant say anything that which car grabs early lead because we dont know the value of constant.

b.) at overtake position both will travel equal distance

using equation of motion

s = ut + 0.5 at^2

0.5 (alpha)t^(-1/2) t^2 = beta *t^2

t = (alpha/beta)^2

not put the value of t in equation

S = ut + 0.5 at^2

S = 0 + 0.5 (alpha)(alpha/beta)^6 or S = 0.5 (beta) (alpha/beta)^4

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