A train accelerates at a₁ and then decelerates at a₂, both in km/min², travelling 4 km in 1/15 h and starting/ending at rest. If (1/a₁ + 1/a₂) = x, find x.
Physics · Mixed Chapter
JEE Main Practice

Question

A train accelerates at a₁ and then decelerates at a₂, both in km/min², travelling 4 km in 1/15 h and starting/ending at rest. If (1/a₁ + 1/a₂) = x, find x.

G1 Physics · Accepted Answer

Step 1: Total time = (1/15)×60 = 4 min. Let maximum speed be v. Step 2: Speed–time graph is triangular, hence distance S = ½vT, so v = 2S/T = 2×4/4 = 2 km/min. Step 3: Acceleration and deceleration times are v/a₁ and v/a₂. Hence T = v(1/a₁ + 1/a₂). Step 4: 1/a₁ + 1/a₂ = 4/2 = 2 min²/km, so x = 2.