a mouse has a constant speed 2m/s. after 20s, a cat moves with acceleration 4m/(s^2).?

 Dм = mouse's displacement (distance traveled).

 Dc = cat's displacement

 Vм = mouse's velocity (constant) = 2 m/sec ... (assumed zero at t = 0)

 Vci = cat's initial velocity = 0

 Ac = cat's acceleration = 4 m/sec² ... (at t = 20 sec)

 Tc = cat's motion time frame relative to mouse's (t)

 Tc = t − 20

 ******* "t" must be ≥ 20 sec

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   Dм = (Vм) • t

   Dм = (2) • t

 Dc = (½) • (Ac) • (Tc)² + (Vci) • (Tc)

 Dc = (½) • (4) • (t − 20)² + (Vci) • (t − 20)

 Dc = (½) • (4) • (t − 20)²

     Dм = Dc

      2t = 2(t − 20)²

       t = t² − 40t + 400

    0 = t² − 41t + 400

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 t = { 41 ± √ [ (-41)² − 4(1)(400) ] } ⁄ 2(1)

 t = { 41 ± 9 } ⁄ 2

 t = 16 sec (disregard)  and  t = 25 sec

 t = 25 sec from when the mouse starts since ******* "t" must be ≥ 20 sec