The graph below shows the velocity versus time graph for a body. Which of the following graphs represents the corresponding acceleration $v/s$ time graph?

Constant acceleration means the slope of the $x-t$ graph is constant. True or False?

The figure shows a velocity-time graph of a particle moving along a straight line. The correct displacement-time graph of the particle is shown as:

The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae are correct for describing the motion of the particle over the time-interval $t_1$ to $t_2$?
$(a)$ $x(t_2) = x(t_1) + v(t_1)(t_2 - t_1) + (1/2)a(t_2 - t_1)^2$
$(b)$ $v(t_2) = v(t_1) + a(t_2 - t_1)$
$(c)$ $v_{\text{average}} = (x(t_2) - x(t_1)) / (t_2 - t_1)$
$(d)$ $a_{\text{average}} = (v(t_2) - v(t_1)) / (t_2 - t_1)$
$(e)$ $x(t_2) = x(t_1) + v_{\text{average}}(t_2 - t_1) + (1/2)a_{\text{average}}(t_2 - t_1)^2$
$(f)$ $x(t_2) - x(t_1) = \text{area under the } v-t \text{ curve bounded by the } t\text{-axis and the dotted lines shown.}$

If the position-time graph of a particle is a sine curve as shown,what will be its velocity-time graph?

The motion of a particle is described by the equation $x = a + bt^2$ where $a = 15 \, cm$ and $b = 3 \, cm/s^2$. Its instantaneous velocity at time $t = 3 \, s$ will be ........ $cm/s$.