A `2144kg` freight car roles along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in figure. Both springs are described by Hooke's law with `k_1=1600Nm^-1` and `k_2=3400Nm^-1`. After the first spring compresses a distance of `30.0cm`, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph in figure. The car comes to rest `50.0cm` after first contracting the two-spring system. Find the car's initial speed `(i n xx10^-1Nm^-1)`.

Answer

`(5)`

Explanation

KE of car converts into elastic potential energy of springs.
`1/2mv^2=1/2k_1(50/100)^2+1/2k_2(20/100)^2`
solve to get `v=0.5ms^-1`