Question

x = 1+t-t², where x is the x coordinate in meters and t is the time.

Find from the given equation:

1) time when the body stops

2) position of the body in 2 seconds

Answer 1

(1) When body stops means its velocity is zero at that time.
$$\begin{gathered} X=1+t-t^2 \\ \frac{dX}{dt}=1-2t \\ Whenbodystops,\frac{dX}{dt}=0,Hencet=0.5 \end{gathered}$$

(2) At time t=2 s
$X=1+2-2^2=-1m$