A cat starts 5 m behind a rat with speed 5 m/s and acceleration 2.5 m/s²; the rat starts from rest with acceleration β. Find β for the cat to overtake the rat.
Physics · Mixed Chapter
JEE Main Practice

Question

A cat starts 5 m behind a rat with speed 5 m/s and acceleration 2.5 m/s²; the rat starts from rest with acceleration β. Find β for the cat to overtake the rat.

G1 Physics · Accepted Answer

Step 1: Set cat displacement x_c = 5t + ½(2.5)t² and rat position x_r = 5 + ½βt². Step 2: Catching condition is ½(2.5−β)t² + 5t − 5 = 0. Step 3: Without specifying a catch time or a limiting condition, β cannot have a unique numerical value. For instance, both β = 2 and β = 3 can allow interception at positive times. The PDF key is 3, but the question is underdetermined.