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

let the mouse start at time t=0

at any time the distance traveled by mouse is given by 2t

The cat starts after 20s with acceleration 4 m/s^2

Distance traveled by cat at time t is 1/2 * a* (t-20)^2 ut+1/2at^2 u =0 and t = t-20

=1/2 *4*(t-20)^2

equating both when they meet

2t = 2(t-20)^2

t = (t-20)^2

t = t^2- 40t +400

t^2 -41t +400 =0

(t-25)(t-16) = 0

ie t = 25 or t =16 t=16 not possible since mouse has not started so t =25

at 2*25 = 50 m distance

the mouse would have travelled 40m in 20s & move further @ 2 m/s

assuming the cat starts from rest, and using the appropriate SUVAT equation

0.5*4t^2 = 40+2t

t^2 - t - 20 = 0

(t-5)(t+4) = 0

taking the +ve value,

t = 5s after it starts = 25s after the mouse starts