Question

In figure shows the x coordinate of a particle as a function of time. Find the sings of vx and ax at t = t1, t = t2 and t = t3.
Figure

Answer 1

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sorry first complete the question and give the figure for the question

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Answer 2

The signs of $v_x$ and $a_x$ at  t = $t_1$,  t = $t_2$ and t = $t_3$ has been found.

Explanation:

If x’ and x” be the x-co-ordinate of particle as a function of initial time t’ and t”  individually,

Then  $v_{x}=\frac{\left(x^{\prime \prime}-x^{\prime}\right)}{\left(t^{\prime \prime}-t^{\prime}\right)}$  $=\tan \theta$        

For ( t”-t’) extremely small it is the  $v_x$ at that instant.  

So slope of the tangent at any point in the above graph gives $v_x$    

At t = $t_1$,  tan θ is +ve, so sign of  $v_x$ is +ve  

At t = $t_2$,  the slope of the curve is horizontal, so tanθ =0 ⇒ $v_x$=0.

At t = $t_3$, the slope of the curve is -ve, so sign of $v_x$ is –ve.

Hence, the signs of $v_x$ and $a_x$ at  t = $t_1$,  t = $t_2$ and t = $t_3$ has calculated.