A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is:
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Question

A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is:

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G1 Physics · Accepted Answer

Step 1: If t₁ is acceleration time and t₂ is deceleration time, vₘₐₓ=αt₁=βt₂. Step 2: Total time t=t₁+t₂=vₘₐₓ(1/α+1/β). Step 3: Hence vₘₐₓ=t/[1/α+1/β]=αβt/(α+β). Final answer: D.