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1.

When a particle moves with constant velocity, its average velocity, its instantaneous velocity and its speed are all equal. Comment on this statement.

Answer»

Constant velocity means that a particle has the same direction and speed at every point. So, its average velocity and instantaneous velocity are equal. Its speed being a scalar quantity is equal in magnitude only.

2.

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 vx  =(x"-x')/(t"-t') = tanθ

For t"-t' infinitesimally small it is the  vx at that instant. 

So slope of the tangent at any point in the above graph gives vx . 

At t=t1, tanθ is positive, so sign of  vx is positive. 

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

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