The position of a particle moving along the $x$ axis is given by the equation $x = (10 + 6t - 3t^2) \ m$. The distance travelled by the particle from $t = 1 \ s$ to $t = 4 \ s$ is: (in $m$)

$A$ particle moves according to the equation $y = a + bt + ct^2 - dt^4$. What are the initial velocity and initial acceleration of the particle?

$m$ mass particle is constrained to move on the $x$-axis. $A$ force $F$ acts on the particle,always pointing toward the equilibrium position $E$. The magnitude of $F$ is constant except at $E$ where it is zero. The particle is displaced a distance $A$ to the left of $E$ and released from rest at $t = 0$. Find the minimum time taken to reach from $x = -A/2$ to $x = 0$.

If a car at rest accelerates uniformly to a speed of $144 \, km/h$ in $20 \, s$,then it covers a distance of ........ $m$.

$A$ student is at a distance of $16 \ m$ from a bus when the bus begins to move with a constant acceleration of $9 \ m \ s^{-2}$. The minimum velocity with which the student should run towards the bus so as to catch it is $\alpha \sqrt{2} \ m \ s^{-1}$. The value of $\alpha$ is

$A$ particle moves a distance $x$ in time $t$ according to the equation $x = (t + 5)^{-1}$. The acceleration of the particle is proportional to: