Question

Question 9. The acceleration of a body from a velocity -time graph is
(a) Is denoted by a line parallel to the time axis at any point on the distance axis
(b) Equal to the slope of the graph
C) Area under the graph
(d) Is denoted by a line parallel to the distance axis at any point on the time axis



Question 10. Distance covered by a body from velocity-time graph is
(a) Is denoted by a line parallel to the distance axis at any point on the time axis
(b) Is denoted by a line parallel to the time axis at any point on the distance axis
(c) Equal to the slope of the graph
(d) Area under the graph
​

Answer 1

9. Acceleration is defined as the rate of change of velocity for a given period of time and is given by:

      $acceleration(a) = \frac{Change\ in\ velocity}{Time}$

In mathematical form,

                         $a =\frac{v}{t}$               ( let v = change in velocity)

                        at = v

           The above equation represents a straight line in the form $y =mx + c$

Where m = slope of the line

              c = constant

Therefore, acceleration represents the slope of the velocity-time graph.

Therefore, The correct option is (b)Equal to the slope of the graph.

10. Distance covered by any  body is given by:

                         distance = speed × time

Therefore, The distance covered by a body can be calculated by measuring the total area under the velocity-time graph.

Therefore, The correct option is (d) Area under the graph.

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Answer 2

9.

Explanation for correct option

b:

1. Acceleration is defined as the rate of change of velocity per unit time.
2. It represents a straight line using equation $y=mx+c$.

Thus, acceleration is the slope of the velocity-time graph.

Explanation for incorrect options

a:

At any point on the distance axis, the acceleration is not denoted by a line parallel to the time axis.

Thus, option a is incorrect.

c:

The area under the graph does not represent the acceleration.

Thus, option c is incorrect.

d:

At any point on the time axis, the acceleration is not denoted by a line parallel to the distance axis.

Thus, option d is also incorrect.

Hence, option b) is correct.

10.

Explanation for correct option

d:

1. Distance can be defined as how much ground an object has covered regardless of its starting or ending point.
2. The distance travelled is represented by the area under the line in a velocity-time graph.

Explanation for incorrect options

a:

Distance is not denoted by a line parallel to the distance axis at any point on the time axis in a velocity-time graph.

Thus, option a is incorrect.

b:

Distance is not denoted by a line parallel to the time axis at any point on the distance axis in a velocity-time graph.

Thus, option b is incorrect.

c:

Distance is not equal to the slope of a velocity-time graph.

Thus, option c is incorrect.

Hence, option d) is correct.

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