A train starting from rest picks up a speed of $10\, m s ^{-1}$ in $100\, s$. It continues to move at the same speed for the next $250\, s$. It is then brought to rest in the nert $50\, s$. Plot a speed$-$time graph for the entire motion of the train.
$(i)$ acceleration of the train while accelerating,
$(ii)$ retardation of the train while retarding,
$(iii)$ and the total distance covered by the train.
A train starting from rest picks up a speed of $10\, m s ^{-1}$ in $100\, s$. It continues to move at the same speed for the next $250\, s$. It is then brought to rest in the nert $50\, s$. Plot a speed$-$time graph for the entire motion of the train.
$(i)$ acceleration of the train while accelerating,
$(ii)$ retardation of the train while retarding,
$(iii)$ and the total distance covered by the train.
The speed$-$time graph is as shown
$(i)$ Acceleration is equal to the slope of the graph
$AB =\frac{ BF }{ AF }=\frac{10}{100}=0.1 m s ^{-2}$
$(ii)$ Retardation is equal to the slope of the graph
$CD =\frac{ CE }{ DE }=\frac{10}{50}=0.2 m s ^{-2}$
$(iii)$ Distance covered during retardation Area of trapezium $ABCD$
$=\frac{1}{2}( AD + BC ) \times BF$
$=\frac{1}{2}(400+250) \times 10=3250 m$
Similar Questions
Write true or false for the following statements
A body is said to be at rest, if it does not change its position with respect to the reference point.
Write true or false for the following statements
A body is said to be at rest, if it does not change its position with respect to the reference point.
Write true or false for the following statements
The motion in animals is called locomotion. Mechanics deals with the motion of non$-$living objects.
Write true or false for the following statements
The motion in animals is called locomotion. Mechanics deals with the motion of non$-$living objects.
Give an example of an accelerated body, moving with a uniform speed.
Give an example of an accelerated body, moving with a uniform speed.
The area under the velocity$-$time graph gives the value of
The area under the velocity$-$time graph gives the value of
The graph given below is the distance$-$time graph of an object.
$(i)$ Find the speed of the object during first four seconds of its journey.
$(ii)$ How long was it stationary ?
$(iii)$ Does it represent a real situation ? Justify your answer.
The graph given below is the distance$-$time graph of an object.
$(i)$ Find the speed of the object during first four seconds of its journey.
$(ii)$ How long was it stationary ?
$(iii)$ Does it represent a real situation ? Justify your answer.