A train moves from one station to another in $2$ hours time. Its speed-time graph during this motion is shown in the figure. The maximum acceleration during the journey is.............$km\, h^{-2}$
$140$
$160$
$100$
$120$
Starting from rest, acceleration of a particle is $a = 2(t - 1).$ The velocity of the particle at $t = 5\,s$ is.........$m/sec$
For a moving body at any instant of time
A particle executes the motion described by $x(t) = x_0 (1 - e^{-\gamma t} )$ ; જ્યાં $t\, \geqslant \,0\,,\,{x_0}\, > \,0$.
$(a)$ Where does the particle start and with what velocity ?
$(b)$ Find maximum and minimum values of $x(t),\, v(t)$ $a(t)$. Show that $x(t)$ and $a(t)$ increase with time and $v(t)$ decreases with time.
Draw $x \to t$ graph for positive acceleration.