In a straight-road car race, car A takes time t less than car B at the finish and passes the finish with speed v more than car B. Both start from rest and move with constant accelerations a₁ and a₂. Then v is:
Options

Question

In a straight-road car race, car A takes time t less than car B at the finish and passes the finish with speed v more than car B. Both start from rest and move with constant accelerations a₁ and a₂. Then v is:

Options

G1 Physics · Accepted Answer

Let finishing times be T₁ for car A and T₂=T₁+t for car B. Equal race distance gives a₁T₁²=a₂T₂², so √a₁T₁=√a₂T₂. The difference of finishing speeds is v=a₁T₁-a₂T₂=t√(a₁a₂). Hence option C.