A 599 g particle moving along the x axis experiences the...

A 599 g particle moving along the x-axis experiences the force shown in picture. The particle's velocity is 1.54 m/s at x=0. What is its velocity at x=1.03 m? (F=4 N, s=1.03 m) What is its velocity at x=2.06 m? What is its velocity at x=3.09 m?

Transcript

00:01 Hi, the first part of the question, we are asked to find out the velocity at x is equal to 2 meters.

00:10 We are provided with velocity at x is equal to 0 as v0 is equal to 3 .4 meter per second.

00:20 The mass is given as 1 kilogram.

00:24 Now, since we have the initial velocity, we can find out the initial kind technology which is given by half m v0 square we just need to substitute the values and solve for it half into one kilogram into velocity is 3 .4 meter per second whole square upon solving this we'll get the final answer as 5 .78 jules this is the initial kinetic energy now we have to understand that the given graph is a force into displacement graph for a force into displacement graph for a force displacement graph the area under the curve is equal to work done we know work done is also equal to change in kind technology now we can understand that from x equal to x equal to x equal to 2 the area under the graph is a rectangle triangle so this work done is equal to change in kind technology will be equal to area of a right angle triangle which is nothing but half into base into height now we just need to substitute the values the base is nothing but 2 meters so we'll substitute it as 2 the height is nothing but 10 newtons so i'll solving this we'll get the change in kinetic energy as 10 jules now we have found out the initial kind energy and the change in kinetic energy so the kinetic energy at x is equal to 2 will be ke2 is equal to sum of the initial kinetic energy plus the change in kindic energy we also know that this k -e2 can be given by half mv2 square is equal to k -e plus delta k e now we have to substitute all the known values and solve for v2 which is the velocity at x is equal to 2 meters so it will be half into mass is 1 kilograms v2 is what you have to find out which is equal to 5 .78 plus 10.

02:47 So we'll get the velocity at x is equal to 2 which is v2 as 5 .6 meter per second.

03:01 So we have the answer for our first subpart.

03:06 Now for the second subpart we need to find out the velocity at x is equal to 4 meters.

03:13 We know the change in kinetic energy is the area under the curve which in this case is some of the right angle triangle above the x -axis and the right angle triangle below the x -axis...

Question

A 599 g particle moving along the x-axis experiences the force shown in picture. The particle's velocity is 1.54 m/s at x=0. What is its velocity at x=1.03 m? (F=4 N, s=1.03 m) What is its velocity at x=2.06 m? What is its velocity at x=3.09 m?

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