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Physics
Motion in one dimension
A particle starts moving from rest under uniform acceleration. It travels a distance $x$ in the first two seconds and a distance y in the next two seconds. If $y=nx$, then $n$ is equal to_____
A) 1
B) 2
C) 3
D) 4
Physics
Motion in one dimension
A three-wheeler starts from rest, accelerates uniformly with \[1m/{s^2}\] on a straight road for \[10s\] , and then moves with uniform velocity. Plot the distance covered by the vehicle during the nth second \[\left( {n = 1,2,3,..} \right)\] versus \[n\] . What do you expect this plot to be during accelerated motion: a straight line or a parabola?
Physics
Motion in one dimension
A race car starts from rest and accelerates uniformly to a speed of $40m{s^{ - 1}}$ in $8.0$ seconds. How far will the car travel during the $8.0$ seconds?
Physics
Motion in one dimension
A car starts from rest with a constant acceleration of $2m.{s^{ - 2}}$ . Determine: (a) the speed at the end of fifth second (b) the distance covered in five seconds (c) the speed after covering $100m$ ?
Physics
Motion in one dimension
If a particle moves along a straight line according to $s\left( t \right) = {t^4} - 4{t^3} + 6{t^2} - 20$, how do you find the maximum & minimum acceleration on $0 \leqslant t \leqslant 3$?
Physics
Motion in one dimension
A body starts from rest and is uniformly accelerated for $30\sec $.The distance covered in first $10\sec $ is \[{x_1}\] , for next $10\sec $ is \[{x_2}\] and for last $10\sec $ is \[{x_3}\] the then the ratio of \[{x_1}:{x_2}:{x_3}\]?
Physics
Motion in one dimension
A train starts from rest and moves with a constant acceleration of $2.0m{s^{ - 2}}$ for half a minute. The brakes are then applied and the train comes to rest in one minute. Find
(a) the total distance moved by the train,
(b) the maximum speed attained by the train and
(c) the position(s) of the train at half the maximum speed.
Physics
Motion in one dimension
The position-time (x-t) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in Fig. above. Choose the correct entries in the brackets below :
(a) A lives closer to the school than B
(b) A starts from the school earlier than B
(c) A walks faster than B
(d) A and B reach home at the same time
(e) A overtakes B on the road twice.
Physics
Motion in one dimension
Can an object be in equilibrium if it is in motion?
Physics
Motion in one dimension
A particle is dropped from the top of a tower $h$ meter high and simultaneously a particle is projected upwards from bottom. They meet when the upper one has descended $\dfrac{1}{n}$ of the distance. Find the initial velocity of the lower particle ?
Physics
Motion in one dimension
A stone is thrown horizontally with velocity $\sqrt {2gh} $ from a top of a tower of height $h$ . Find where it will strike the level ground through the foot of the tower. What will be its striking velocity?
Physics
Motion in one dimension
Two particles having position vectors \[{\vec r_1} = \left( {3\hat i + 5\hat j} \right)\] and \[{\vec r_2} = \left( { - 5\hat i - 3\hat j} \right)\] are moving with velocities \[{\vec v_1} = \left( {4\hat i + 3\hat j} \right)\] and \[{\vec v_2} = \left( {\alpha \hat i + 7\hat j} \right)\] If they collide after 2 seconds, the value of a is
A. \[2\]
B. \[4\]
C. \[6\]
D. \[ - 8\]
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