Explanation
In ‘s — t’ graph (Position-time)
The straight line parallel with time axis represent state of rest.
Up to time t1 slope of the graph is Constant and after t1 slope is zero i. e., the body travel with constant speed up to time t1 and then stops.
Because acceleration due to gravity is constant so the slope of line will be constant i. e. ,velocity time curve for a body projected vertically upwards in straight line.
Slope of displacement time graph is negative only at point E
Since slope of graph remains constant for velocity-time graph.
Other graph shows more than one velocity of the particle at single instant of time which is not practically possible.
Slope of velocity-time graph measure acceleration. For graph (a) slope is zero. Hence a = 0 i. e., motion is uniform.
From acceleration time graph, acceleration is constant for first part of motion so, for this part velocity of body increases uniformly with rime and as a = 0 then the velocity becomes constant. Then again increased because of constant acceleration.
I is not possible because total distance covered by a particle increases with time.
Ills not possible because at a particular time, position cannot have two values.
III is not possible because at a particular time, velocity cannot have two values.
IV is not possible because speed can never be negative.
When body going vertically upwards, reaches at the highest point, then it is momentarily at rest and it then reverses its direction. At the highest point of motion, its velocity is zero but its acceleration is equal to acceleration due to gravity.
As motion is governed by force of gravity and acceleration due to gravity (g) is independent of mass of object.
When a body falling freely, only gravitational force acts on it in vertically downward direction. Due to this downward acceleration the velocity of a body increases and will he maximum when the body touches the ground.
As displacement is either smaller or equal to distance but never be greater than distance.
Since velocity is a vector quantity, hence as its direction changes keeping magnitude constant, velocity is said to be changed. But for constant speed in equal time interval distance travelled should be equal.
Speedometer measures instantaneous speed of automobile.
Negative slope of position time graph represents that the body is moving towards the negative direction and if the slope of the graph decrease with time then it represents the decrease in speed i. e., retardation in motion.
A body having positive acceleration can be associated with slowing down, as time rate of change of velocity decrease, but velocity increases with time, from graph it is clear that slope with time axis decreases, but velocity increases with time.
A body having negative acceleration can be associated with a speeding up, if object moves along negative X-direction with increasing speed.
Motion of rocket is based on action reaction phenomena and is governed by rate of fuel burning causing the change in momentum of ejected gas.
If the position-time graph of a body moving uniformly is a straight line parallel to position axis, it means that the position of body is changing at constant time. The statement is abrupt and shows that the velocity of body is infinite.
Position-time graph for a stationary object is a straight line parallel to time axis showing that no change in position with time.
Since slope of displacement-time graph measures velocity of an object.
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