A car accelerates from rest with constant acceleration a for time t1, then decelerates at constant rate b to come to rest. If total elapsed time is T, what is the total distance covered?
Answer and explanation
Correct answer: D. (1/2) [a b / (a + b)] T^2
- Step 1: Maximum velocity reached v_max = a t1 = b t2, where t1 + t2 = T.
- Step 2: t1 = T * b / (a + b) => v_max = [a b / (a + b)] T.
- Step 3: Velocity-time graph is a triangle with base T and height v_max.
- Step 4: Distance = (1/2) Base Height = (1/2) T * v_max = (1/2) [a b / (a + b)] T^2.
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