The displacement of a particle after time $t$ is given by $x = \left( {k/{b^2}} \right)\left( {1 - {e^{ - bt}}} \right)$ where $b$ is a constant. What is the acceleration of the particle? 

A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2=1+t^2$. Its acceleration at any time $\mathrm{t}$ is $\mathrm{x}^{-\mathrm{n}}$ where $\mathrm{n}=$ . . . . .

Draw $x \to t$ graph for zero acceleration.

A particle moves in a straight line and its position $x$ at time $t$ is given by $x^2=2+t$. Its acceleration is given by

The velocity of a particle moving in the positive direction of $x$-axis varies as $v=5 \sqrt{x}$. Assuming that at $t=0$, particle was at $x=0$. What is the acceleration of the particle $.........m/s^2$

A car, moving with a speed of $50 \,km/hr$, can be stopped by brakes after at least $6\,m$. If the same car is moving at a speed of $100 \,km/hr$, the minimum stopping distance is..........$m$