A car moving along a straight highway with a speed of 126 kilometre per hour is brought to a stop within a distance of 200m. What is the retardation of the car (assumed uniform) and how long does it taken for the car to stop?

A car moving along a straight highway with a speed of 126 kilometre pe

1.	A car moving along a straight highway with a speed of 126 kilometre per hour is brought to a stop within a distance of 200m. What is the retardation of the car (assumed uniform) and how long does it taken for the car to stop?
Answer» Solution :INITIAL VELOCITY of car, `U=126kmh^(-1)=126xx(5)/(6)ms^(-1)=35ms^(-1)""………(1)` Since, the car finaly comes to rest, v=0 Distance covered, s 200 m, a=?, t=? `v^(2)=u^(2)-2asora=(v^(2)-u^(2))/(2s)""......(2)` Substituting the values from EQ. (1) in eq. (2), we get `a=(0-(35)^(2))/(2xx200)=-(35xx35)/(400)=-(46)/(16)ms^(-2)=-3.06ms^(-2)` Negative sign shows that acceleration in negative which is CALLED retardation, uniformly retarded at `-a=3.06ms^(-2)`. To find t, let us use the relation v=u+at `t=(v-u)/(a)` Use `a=-3.06ms^(-2),v=0,u=35ms^(-1)` `:.t=(v-u)/(a)=(0-35)/(-3.06)=11.44s` `:.t=11.44` sec.