Figure (3-Q1) shows the x- coordinate of a particle as a function of t

1.	Figure (3-Q1) shows the x- coordinate of a particle as a function of time. Find the signs of vx and ax at t=t1, t= t2 and t=t3.
Answer» If x' and x" be the x-coordinate of the particle at initial time t' and t" respectively then v_x =(x"-x')/(t"-t') = tanθ. For t"-t' infinitesimally 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=t₁, tanθ is positive, so sign of v_x is positive. At t= t₂ the slope of the curve is horizontal, so tanθ=0 → v_x =0. At t=t₃ the slope of the curve is negative, so sign of v_x is negative.

Figure (3-Q1) shows the x- coordinate of a particle as a function of time. Find the signs of vx and ax at t=t1, t= t2 and t=t3.

Answer»

If x' and x" be the x-coordinate of the particle at initial time t' and t" respectively then v_x =(x"-x')/(t"-t') = tanθ.

For t"-t' infinitesimally 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=t₁, tanθ is positive, so sign of v_x is positive.

At t= t₂ the slope of the curve is horizontal, so tanθ=0 → v_x =0.

At t=t₃ the slope of the curve is negative, so sign of v_x is negative.