In kinematics, a velocity-time graph can be used to analyze particle motion by plotting velocity on the y-axis and time on the x-axis, where the slope of the graph represents acceleration; for a particle with initial velocity of 2 m/s due west and acceleration of 1 m/s² due east, the velocity at t=6 seconds is calculated as 4 m/s using the formula v = u + at, with the graph showing the particle initially moving west, coming to rest, and then accelerating eastward.
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vel-time graph in kinematics prob..#shorts #jeemains #kinematics #graph #physics #neet #class11Added:
reference line, this is indicating east.
Positive x, this is the west, right?
Positive x direction is referring east, minus west.
Towards positive y axis, this direction we identify with north and downward we identify with south.
Right?
So, it is said that initial velocity 2 m/s due west, that means this direction.
So, a particle is having initial velocity this way.
That is of magnitude 2 m/s and it is having an acceleration on it is 1 m/s due east.
Right? Acceleration is suggested 1 m/s² due east. Okay?
So, now we have been asked about the velocity of the particle at t equal to 6 second. So, velocity formula wise u plus at.
We will apply the value of u as minus 2 provided if we take towards positive direction positive, then the opposite one has to be direction wise referred negative.
Right? So, initial direction minus 2 plus 1 into 6. So, minus 2 plus 6 is 4 m/s.
So, at t equal to 6 second, the velocity will be magnitude equally 4 and it should come positive. That means actually body is starting at t equal to 0 here. It is since it is having an initial velocity of 2 m/s this and acceleration of 1 m/s² this way, so that does mean that does mean the body is initially going for a certain period of time this way and then it is returning back. So, motion will take place like this. First, it is going backward against the opposite direction acceleration velocity will become zero, right? Velocity will uh zero and then uh due to the continuous presence of acceleration now that will pull the mass right word, right? Right. So, if I try to draw the V versus T graph, right, this is being the velocity, this is the time. So, initial velocity is suggested to be negative, right? So, we should start from some negative mark of velocity. This is the zero zero position, right? From here upward is positive velocity, downward is negative, so I can mark minus two means it is somewhere here, right?
And uh it is being uh I said slope of V versus T graph will represent acceleration. Acceleration being positive, so I can draw it like this.
Okay, so the graph will be drawn from negative Y axis, which is indicating the negative velocity. It will cross the time axis and go up to that uh positive value. If I mark this positive value is four, right? So, then this uh point on X X that is the time, that is this 6 second.
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