Acceleration versus velocity graph of a particle moving in a straight line starting from rest is as shown in figure. The corresponding velocity-time graph would be

“Explain average acceleration and instantaneous acceleration.”

The acceleration of a particle which moves along the positive $x-$axis varies with its position as shown. If the velocity of the particle is $0.8 m/s$ at $x = 0$ , the velocity of the particle at $x = 1.4$ is(in $m/s$)

A particle starts from the origin at $t=0$ $s$ with a velocity of $10.0 \hat{ j } \;m / s$ and moves in the $x-y$ plane with a constant acceleration of $(8.0 \hat{ i }+2.0 \hat{ j }) \;m \,s ^{-2} .$

$(a)$ At what time is the $x$ - coordinate of the particle $16\; m ?$ What is the $y$ -coordinate of the particle at that time?

$(b)$ What is the speed of the particle at the time?

The displacement $x$ of a particle depend on time $t$ as $x = \alpha {t^{^2}} - \beta {t^3}$ 

A rigid rod is sliding. At some instant position of the rod is as shown in the figure. End $A$ has constant velocity $v_0$. At $t = 0, y = l$ .