Figure shows the velocity vs time graph for a particle...

Figure shows the velocity vs. time graph for a particle moving along the x-axis. Its initial position is 2.0 m at t=0 s. What are the particle's position, velocity, and acceleration at t=1.0 s? What are the particle's position, velocity, and acceleration at t=3.0 s? (m/s)

Transcript

00:01 Hello and welcome to this video solution of numerate.

00:04 So if we are given a velocity time graph, let me just draw a simple one.

00:10 So it starts it's four meters and then it goes down till and right.

00:18 So here we have got the velocity along y -axis and this time along x -axis, right? so this is zero, this is two meters per second and this is four meters per second and this point is at two whereas this point is is at 4 right this is 3 and this is 1 and this 3 time is in second and the velocity is meter per second right it's given that the initial position x -not is at 2 meters per 2 meters at t equal to 0 now you have to calculate the particles position uh velocity and acceleration at t at 1 right so three things right position you have to find out to find out the position you need to find out the distance d 1 okay first of all let's say t equal to one second we need to find everything right so the displacement d will be equal to the area under this velocity time graph from 0 to 1 second so this is pretty simple so 4 times of 1 right 4 is a height and 1 is a distance so this rectangle will have a displacement of 4 meters right so the total distance x 1 we can take which is equal to x0 plus d so 4 plus 2 right which is 6 meters is a displacement you have next next you have got to have the velocity v1, which is nothing but 4 meters per second, clearly from this graph itself, right? the acceleration a1 will be 0 because if you see over this entire period, the velocity is constant, right? so you have got these three parameters already mentioned, right? now similar, the same thing you have to find out for t equal to three seconds, right? now for 3 equal to 3, what you need to do is you need to find out the again the displacement and that displacement...

Question

Figure shows the velocity vs. time graph for a particle moving along the x-axis. Its initial position is 2.0 m at t=0 s. What are the particle's position, velocity, and acceleration at t=1.0 s? What are the particle's position, velocity, and acceleration at t=3.0 s? (m/s)

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