If the velocity of a particle is $(10 + 2t^2) \ m/s$,then the average acceleration of the particle between $2 \ s$ and $5 \ s$ is..........$m/s^2$.

$A$ particle is moving in one dimension (along $x$-axis) under the action of a variable force. Its initial position was $16 \,m$ right of the origin. The variation of its position $(x)$ with time $(t)$ is given as $x = -3t^3 + 18t^2 + 16t$,where $x$ is in $m$ and $t$ is in $s$. The velocity of the particle when its acceleration becomes zero is . . . . . . $m/s$.

Each of the three graphs represents acceleration versus time for an object that already has a positive velocity at time $t_1$. Which graphs show an object whose speed is increasing for the entire time interval between $t_1$ and $t_2$?

The position,velocity,and acceleration of a particle moving with a constant acceleration can be represented by:

Let $v$ and $a$ denote the velocity and acceleration respectively of a particle in one-dimensional motion. Which of the following statements is correct?

The distance travelled by a body moving along a line in time $t$ is proportional to $t^3$. The acceleration-time $(a, t)$ graph for the motion of the body will be