A $150 \,m$ long train is moving with a uniform velocity of $45 \,km/h$. The time taken by the train to cross a bridge of length $850 $ meters is..........$sec$
$56$
$68$
$80 $
$92$
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.......$km/h$
The ratio of the numerical values of the average velocity and average speed of a body is always
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].
A man walks on a straight road from his home to a market $2.5\; km$ away with a speed of $5 \;km h ^{-1} .$ Finding the market closed, he instantly turns and walks back home with a speed of $7.5 \;km h ^{-1} .$ What is the average speed of the man over the interval of time $0$ to $40\; min$ ?
A ball thrown up from a location, returns back at the same location. Which of the following statements are correct.
$(a)$ Distance travelled by ball can be zero
$(b)$ Displacement of ball is zero
$(c)$ Average velocity of ball is zero
$(d)$ Acceleration of the ball is zero