Two particles $P$ and $Q$ simultaneously start moving from point $A$ with velocities $15\,m/s$ and $20\,m/s$ respectively. The two particles move with accelerations equal in magnitude but opposite in direction. When $P$ overtakes $Q$ at $B$,then its velocity is $30\,m/s$. The velocity of $Q$ at point $B$ will be $..........\,m/s$.

The relation between time $t$ and distance $x$ is $t = \alpha x^2 + \beta x$,where $\alpha$ and $\beta$ are constants. The relation between acceleration $a$ and velocity $v$ is:

Two masses of $3.4 \text{ kg}$ and $2.5 \text{ kg}$ are accelerated from an initial speed of $5 \text{ m/s}$ and $12 \text{ m/s}$, respectively. The distances traversed by the masses in the $5^{th}$ second are $104 \text{ m}$ and $129 \text{ m}$, respectively. The ratio of their momenta after $10 \text{ s}$ is $\frac{x}{8}$. The value of $x$ is . . . . . . .

$A$ car accelerates from rest with $2 \,m/s^2$ on a straight line path and then comes to rest after applying brakes. Total distance travelled by the car is $100 \,m$ in $20 \,s$. Then, the maximum velocity attained by the car is (in $\,m/s$)

$A$ particle is constrained to move on a straight line path. It returns to the starting point after $10\, s$. The total distance covered by the particle during this time is $30\, m$. Which of the following statements about the motion of the particle is false?

Let $v$ and $a$ denote the velocity and acceleration respectively of a body. Which of the following statements is correct?