What will be change in speed of moving object if both speed and acceleration are positive or negative ?

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.

A bullet fired into a fixed target loses half of its velocity after penetrating $1\,cm.$ How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion

The velocity-displacement graph of a particle is shown in the figure.

The acceleration-displacement graph of the same particle is represented by :

Your friend driving his car overtakes your car on the highway. Which of the following statement must be true at the instant he is passing you? Assume the cars as point particles.

A motorist starting a car from rest accelerates uniformly to a speed of $v\, m/s$ in $9\, seconds$. He maintains this speed for another $50\, seconds$ and then applies the brakes and decelerates uniformly to rest. His deceleration is numberically equal to three times his previous acceleration. Then the time during which the deceleration takes place is ..........$s$ :-