Between the two stations a train accelerates uniformly at first, then moves with constant velocity and finally retards uniformly. If the ratio of the time taken be $1 : 8 : 1$ and the maximum speed attained be $60\,km/h,$ then what is the average speed over the whole journey.......$km/h$

Position-time graph for a particle is shown in figure. Starting from $t=0$, at what time $t$ is ......... $s$, the average velocity is zero

Explain clearly, with examples, the distinction between 

$(a)$ magnitude of displacement (somettmes called distance) over an interval of time, and the total length of path covered by a particle over the same interval

$(b)$ magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval].

Show in both $(a)$ and $(b)$ that the second quantity is either greater than or equal to the first. When is the equality sign true ? [For simplicity, consider one-dimensional motion only].

Which informations cannot be drawn from average velocity ?

A particle moves for $20 \,seconds$ with velocity $3 \,m/s$ and then velocity $4\, m/s$ for another $20 \,seconds$ and finally moves with velocity $5 \,m/s$ for next $20\, seconds$. What is the average velocity of the particle..........$m/s$

A car moves from $X$ to $Y$ with a uniform speed $v_1$ and returns to $Y$ with a uniform speed $v_2$ . The average speed for this round trip is