$A$ particle starts from rest. Its acceleration $(a)$ versus time $(t)$ graph is as shown in the figure. The maximum speed of the particle will be (in $m \ s^{-1}$)

The displacement equation for a particle is $s = 3t^3 + 7t^2 + 14t + 8 \ m$. Its acceleration at time $t = 1 \ s$ is ....... $m/s^2$.

The motion of a particle along a straight line is described by the function $x = (2t - 3)^2$,where $x$ is in metres and $t$ is in seconds. The acceleration of the particle at $t = 2 \,s$ is (in $\,m/s^2$)

Will the acceleration increase or decrease with an increase in velocity?

The acceleration of a particle which moves along the positive $x$-axis varies with its position as shown in the figure. If the velocity of the particle is $0.8 \,ms^{-1}$ at $x=0$, then its velocity at $x=1.4 \,m$ is (in $ms^{-1}$)

Suggest a suitable physical situation for the following $a-t$ graph.