Two cars start simultaneously from A to B with the same initial speed. Car 1 moves uniformly along the straight line AB. Car 2 moves along a semicircular bypass connecting A and B, with speed increasing uniformly so that at the end its speed is doubled. Which car arrives earlier?
Options

Question

Two cars start simultaneously from A to B with the same initial speed. Car 1 moves uniformly along the straight line AB. Car 2 moves along a semicircular bypass connecting A and B, with speed increasing uniformly so that at the end its speed is doubled. Which car arrives earlier?

Options

G1 Physics · Accepted Answer

Car 1 travels chord AB=2R at speed v, so t₁=2R/v. Car 2 travels semicircle πR with speed increasing uniformly from v to 2v, so average speed=3v/2 and t₂=πR/(3v/2)=2πR/(3v). Since 2π/3>2, t₂>t₁. Car 1 arrives first. Hence option A.