Displacement or Distance (s) = Speed or Velocity (v) * Time (t).
Difference
between Distance and Displacement:
However, in CAT problems, displacement is not used and distance is
usually mentioned. So, we have to use Distance = Displacement. Same for
velocity and speed.
Relative Motion:
When two bodies move in the same direction, relative speed = |difference of speeds|.
The direction of relative speed is in the direction of the two bodies.
When two bodies move in the opposite direction, relative speed = sum of speeds. The direction of relative speed is in the direction of the faster bodies.
When two bodies move in the opposite direction, relative speed = sum of speeds. The direction of relative speed is in the direction of the faster bodies.
Total distance covered by two bodies at a distance D when they are moving
towards each other and they meet each other for the n-th time = (2*n – 1) * D.
When two bodies move towards the same direction, for the n-th meeting, they
need to cover n*2D distance.
Individually, the bodies cover a distance in the ratio of their speeds.
Individually, the bodies cover a distance in the ratio of their speeds.
Boats :
At first, we consider downstream motion of the boat in water.
Say the boat has a velocity b of it’s own, i.e., velocity of boat in still water is b and the river has a velocity r (speed of river current). The downstream speed of the boat be D and the upstream speed be U.
D = ( b + r ). U = (b – r ). b = (D + U )/2. r = (D – U)/2.
Say the boat has a velocity b of it’s own, i.e., velocity of boat in still water is b and the river has a velocity r (speed of river current). The downstream speed of the boat be D and the upstream speed be U.
D = ( b + r ). U = (b – r ). b = (D + U )/2. r = (D – U)/2.
Trains moving in opposite direction have relative speed equal to the sum
of the individual speeds.
Trains moving in the same direction have relative speed equal to the difference of their speeds.
Distance to be covered to cross each other = Sum of the lengths of the trains
Distance covered to cross any stationary object = Length of train + Length of the object. If length of object is very small like in the case the object is a pole or a man, the distance covered b the train is equal to the length of the train.
Trains moving in the same direction have relative speed equal to the difference of their speeds.
Distance to be covered to cross each other = Sum of the lengths of the trains
Distance covered to cross any stationary object = Length of train + Length of the object. If length of object is very small like in the case the object is a pole or a man, the distance covered b the train is equal to the length of the train.
Circular motion:
Bodies moving in opposite direction has relative speed equal to the sum of
their individual speeds. When bodies move in the same direction, the relative
speed is equal to the difference of their individual speeds.
Time taken to meet for the first time = (length of circular track)/(relative speed)
If there are more than two runners and say the fastest runner is S and time taken by T to meet S for the first time = a, for U is b, for V is c, and so on, then time taken for all of them to meet for the first time = L.C.M. ( a. b, c, …).
Time taken to meet for the first time = (length of circular track)/(relative speed)
If there are more than two runners and say the fastest runner is S and time taken by T to meet S for the first time = a, for U is b, for V is c, and so on, then time taken for all of them to meet for the first time = L.C.M. ( a. b, c, …).
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