$A$ particle starts from rest,accelerates at $2 \, m/s^2$ for $10 \, s$,then moves at a constant speed for $30 \, s$,and finally decelerates at $4 \, m/s^2$ until it stops. What is the total distance travelled by it in $m$?

At time $t=0$, a particle leaves the origin and moves in the positive direction of the $X$-axis. If the velocity of the particle varies as $v(t)=v_0(1-t/t_0)$, where $|v_0|=10 \ m/s$ and $t_0=10 \ s$, then the distance covered by the particle during the first $20 \ s$ is: (in $m$)

$A$ 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 moves along a straight line such that its displacement $x$ varies with time $t$ as $x = \alpha t^3 + \beta t^2 + \gamma$, where $\alpha, \beta, \gamma$ are constants. $V_1$ is the average velocity of the particle during its journey between $t = 1 \ s$ and $t = 3 \ s$. $V_2$ is the instantaneous velocity of the particle at $t = 3 \ s$. The ratio $\frac{V_1}{V_2}$ is

Assertion $(A)$: The angle between acceleration and velocity of a body in one-dimensional motion is always zero. Reason $(R)$: One-dimensional motion is along a straight line.

$A$ body is at rest at $x=0$. At $t=0$,it starts moving in the positive $x-$direction with a constant acceleration. At the same instant,another body passes through $x=0$ moving in the positive $x$ direction with a constant speed. The position of the first body is given by $x_{1}(t)$ after time $t$ and that of the second body by $x_{2}(t)$ after the same time interval. Which of the following graphs correctly describes $(x_{1}-x_{2})$ as a function of time $t$?