Question $3.$ The cart shown in figure below moves with constant deceleration changing the

speed from $v0=5\frac{m}{s}$ to $v1=1\frac{m}{s}.$

After $2$ seconds when it reaches the speed $v1$ it suddenly stops.

Write the displacement of the mass as a function of time. Mass $m$ moves without friction on the

surface of the cart. Assume positive direction from left to right $($direction of motion of the cart$).$

Numerical values:

$m=2kg,k=1\mathrm{.}152k\frac{N}{m}.$

Ans: $x(t)=3\mathrm{.}472cos24t+41\mathrm{.}6sin24t(mm)$