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We need to find that How long is the glider in contact with the spring.

We have to find $鈻�t$because of the glider is in contact with spring at the time of impulse localid="1649920534377" $鈻�t$.

For a short time a object receives a force is known as impulse. and under the area the curve of the force-versus-time graph and it is the same as momentum. The impulse is the quantity $J_x$and it is given by equation in the form

$$\begin{gathered} impulse=J_x={鈭�}_{t_i}^{t_f}{F}_x\left(t\right)dt \\ =areaunderthe{F}_x\left(t\right)curvebetween{t}_{i}and{t}_f\left(1\right) \end{gathered}$$

In a graph of force versus time the force is in the range of time $鈻�t$. the impulse takes the rectangle shape, where height is $h=36N$and and the base is $b=鈻�t$. The area of the rectangle is half the product of the heightand the base

$A=\frac{1}{2}\left(height\right)\left(base\right)$

Using equation $\left(1\right)$to get impulse

$$\begin{gathered} J_x=\frac{1}{2}\left(height\right)\left(base\right) \\ =\frac{1}{2}(36N)鈻�t \\ =18鈻�t \end{gathered}$$

After finding impulse $J_x=18鈻�t$.An impulse is the quantity $J_x$that is delivered by a force to an object with an initial momentum $p_{ix}$that changes its momentum $p_{fx}$, and it is given by equation in the form of a force.

$p_{fx}=p_{ix}+J_x\left(2\right)$

THe momentum is given by equation in the form

$p=mv$

By using the momentum $p$and impulse $J_x$expressions in equation (2), we can find an expression for the time $鈻�t$as follows

$$\begin{gathered} p_{fx}=p_{ix}+J_x \\ m{v}_f=m{v}_i+18鈻�t \\ 鈻�t=\frac{m(v_f-v_i)}{18}\left(3\right) \end{gathered}$$

In a graph of velocity versus time the initial speed is $v_i=-3m/s$and final velocity $v_f=3m/s$.

So puttin values into equation $\left(3\right)$for the mass $m,v_{i}and{v}_f$ to get $鈻�t$

$$\begin{gathered} 鈻�t=\frac{m(v_f-v_i)}{18} \\ =\frac{\left(0.60kg\right)\left(3.0m/s-\left(-3.0m/s\right)\right)}{18} \\ =0.2s \end{gathered}$$