Cars A and B move on the same straight road in the same direction. At t=0, A is 120 m behind B. Their speeds are 30 m/s and 20 m/s respectively. From t=0, B accelerates uniformly at 2 m/s². What minimum constant acceleration must A have so that A just touches the limiting condition of overtaking B (minimum separation becomes zero)?
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Question

Cars A and B move on the same straight road in the same direction. At t=0, A is 120 m behind B. Their speeds are 30 m/s and 20 m/s respectively. From t=0, B accelerates uniformly at 2 m/s². What minimum constant acceleration must A have so that A just touches the limiting condition of overtaking B (minimum separation becomes zero)?

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G1 Physics · Accepted Answer

Relative separation s=120−10t+(1/2)(2−a)t². For the limiting case s has a double root, so discriminant is zero: 100−4×120×(2−a)/2=0 ⇒ 100−240(2−a)=0 ⇒ a=29/12 m/s².