Question

Dan is unhappy about a water balloon incident and comes looking for you with ice water. When he finds you you are 9 m apart. He immediately starts running towards you at a constant 4 m/s. You are stuck in a go-cart so you instantly apply full throttle heading away from Dan. The cart starts from rest with uniform acceleration. Dan is hoping to pass you and throw the bucket of ice water in your face. What acceleration must the car have to prevent him from doing such a terrible deed (in m/s^2)?

Answer 1

Answer: For you to prevent that thing you should run atleast with the same speed as that of Dan.

So, v=at

where v = 4m/s

at=4 , so when time will be t you will gain same speed as that of Dan.

Now we will equate the distance between the two so that we can find min acceleration at which he can come just near to you,

(1/2)at^{​​​​​2}​ + 9 = 4t

Now we know at=4 ,

So, 2t + 9 = 4t

2t=9

t=4.5s

So a=4/4.5

a= 0.88 m/s^{​​​​​​2}​​​

Hence, you should have acceleration greater than 0.88 m/s^{​​​​​​2}​​​ to avoid that terrible deed happening to you.