Question

As an object moves along the x axis, many measurements are made of its position, enough to generate a smooth, accurate graph of x versus t. Which of the following quantities for the object cannot be obtained from this graph alone? (Select all that apply.)
the displacement during some time interval
the speed at any instant
the velocity at any instant
the average velocity during some time interval
the acceleration at any instant

Answer 1

The best and most correct answers among the choices provided by your question are he second and third choices. 
The velocity at any instant the average velocity during some time interval cannot be obtained from the graph alone.


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Answer 2

Answer:

the acceleration at any instant

Explanation:

1). the displacement during some time interval

We can determine the displacement of the object from the graph because we know that displacement is defined as the change in position of the object and from graph change in position can be obtained easily

2). the speed at any instant

3). the velocity at any instant

speed at any instant of time and velocity at any instant of time must be same in the magnitude and we can determine it by the slope of the graph

As we know that instantaneous velocity is defined as

$v = \frac{dx}{dt}$

so slope of the graph at any instant will give an idea about instantaneous speed of velocity

4). the average velocity during some time interval

To find average velocity we need the displacement of object at a given interval of time and ratio of this displacement and time interval is known as average velocity

So we can find it from graph

5). the acceleration at any instant

To find the instantaneous acceleration we need to find

$a = \frac{dv}{dt}$

this is not possible to find from x-t graph because in order to find this slope we need to find velocity time graph.