$A$ body travels $102.5 \ m$ in the $n^{\text{th}}$ second and $115.0 \ m$ in the $(n+2)^{\text{th}}$ second. The acceleration is: (in $m/s^2$)

The initial velocity of a particle is $u$ at $t=0$ and the acceleration $a$ is given by $a = \alpha t^{3/2}$. Which of the following relations is valid?

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement $(s)-$ velocity $(v)$ graph of this object is

An object accelerates from rest to a velocity $27.5 \,m/s$ in $10 \,s$. Find the distance covered by the object in the next $10 \,s$ (in $m$).

$A$ particle starts from rest at $x=0 \, m$ with an acceleration of $1 \, m/s^2$. At $t = 5 \, s$,it receives an additional acceleration in the same direction as its motion. At $t = 10 \, s$,its speed and position are $v$ and $x$,respectively. Had the additional acceleration not been provided,its speed and position would have been $v_0$ and $x_0$,respectively. It is found that $x - x_0 = 12.5 \, m$. Then one can conclude that $v - v_0$ is .............. $m/s$.

$A$ $100\, m$ long train is moving with a uniform velocity of $45\, km/hr$. The time taken by the train to cross a bridge of length $1\, km$ is.........$s$