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 $\mathrm{n}=$ . . . . .

Velocity-displacement graph of a particle moving in a straight line is as shown in figure

$Assertion$ : A body can have acceleration even if its velocity is zero at a given instant of time.

$Reason$ : A body is numerically at rest when it reverses its direction.

A car moving along a straight highway with speed of $126 \;\mathrm{km} h^{-1}$ is brought to a stop within a distance of $200\; \mathrm{m}$. how long(in $seconds$) does it take for the car to stop?

The distance travelled by a particle is directly proportional to $t^{1/2}$, where $t =$ time elapsed. What is the nature of motion ?

A car accelerates from rest at a constant rate $\alpha $ for some time, after which it decelerates at a constant rate $\beta $ and comes to rest. If the total time elapsed is $t$, then the maximum velocity acquired by the car is