In the following displacement $x$ versus time $t$ graph,at which among the points $P, Q$ and $R$ is the object's speed increasing?

The displacement $x$ of a particle varies with time $t$ as $x = a e^{-\alpha t} + b e^{\beta t}$,where $a, b, \alpha, \text{and } \beta$ are positive constants. The velocity of the particle will:

The acceleration-time graph for a particle is given. What will be the corresponding velocity-time graph?

The area $A$ of a blot of ink is growing such that after $t$ seconds its area is given by $A = (3t^2 + 7) \, cm^2$. Calculate the rate of increase of area at $t = 2 \, s$. .......... $cm^2/s$

We have carefully distinguished between average speed and magnitude of average velocity. No such distinction is necessary when we consider instantaneous speed and magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why?

The velocity $(v)$-time $(t)$ graph for a particle moving along the $x$-axis is shown in the figure. The corresponding position $(x)$-time $(t)$ graph is best represented by: