A man is 45 m behind the bus when the bus start accelerating from rest with acceleration 2.5 ms-2. With what minimum velocity should the man start running to catch the bus?

Let the man will catch the bus after t second. So, he will cover distance ut.Similarly, distance travelled by the bus will be 12at2.For the given condition,                     ut=45+12at2=45+1.25t2  (As, a=2.5 ms-2  ⇒     u=45t+1.25tTo find the minimum" value of u           dudt=0⇒dudt=-45t2+1.25=0So, we get t = 6s, then u=456+(1.25×6)=15 ms-1