Question

please answer with steps​

Answer 1

Let the bus travel the distance x

Let the bus travel the distance x then, distance travelled by the man, before he would catch the bus=d+x

Let the bus travel the distance x then, distance travelled by the man, before he would catch the bus=d+xtime taken by man to catch the bus=(d+x)/u

for bus

distance travelled=x

acceleration=a

u=0

x=(1/2)×a×t^2

t^2=2x/a

t=√2x/√a

time taken by a man to get the bus=time in which bus covers a distance x

2x/a=(d+x)^2/u^2

2x/a=(d^2+x^2+2dx)/u^2

2xu^2=ad^2+ax^2+2adx

ax^2+2adx-2xu^2+ad^2=0

ax^2+(2ad-u^2)x+ad^2=0

for this equation to satisfy,,,

b^2-4ac should not equal to negative

b^2-4ac should not equal to negativeit can be 0 or greater than0

Now,here

b=2ad-u^2

c=ad^2

b^2-4ac=>(2ad-u^2)^2-4a^2d^2>=0

4a^2d^2+u^4-4adu^2-4a^2d^2>=0

u^4>=4adu^2

u^2/4a>=d

Hence option d) is the correct one

{hope it helps}