You are conducting an experiment inside a train car that may move along level rail tracks. a load is hung from the ceiling on a string. the load is not swinging, and the string is observed to make a constant angle of 45∘ with the horizontal. no other forces are acting on the load. which of the following statements are correct? check all that apply. 1 the train is an inertial frame of reference. 2 the train is not an inertial frame of reference. 3 the train may be instantaneously at rest. 4 the train may be moving at a constant speed in a straight line. 5 the train may be moving at a constant speed in a circle. 6 the train must be speeding up. 7 the train must be slowing down. 8 the train must be accelerating.

Here the weight is hung from the thread inside the ceiling of train

now the FBD of train is analysed

We can say

now by ratio of two equations we have

this shows that train must be in accelerating condition due to which the thread is making an angle with the vertical

now we will have

2 The train is not an inertial frame of reference.

Since train is accelerating so it must be non inertial frame

5 The train may be moving at a constant speed in a circle.

Since its moving in circle so it is in accelerating condition

8 The train must be accelerating.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

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explanation: