Question

Statement I- Integral is used for finding velocity of a moving particle when the distance traversed at any time t is known.
Statement II- Integral is also used in calculating the distance traversed when the velocity at time t is known.
a) Statement I is true; statement II is true; statement II is a correct explanation for statement I
b) Statement I is true; statement II is true; statement II is not a correct explanation for statement I
c) Statement I is true; statement II is false
d) Statement I is false; statement II is true

Answer 1

Hint: Derivation of function of variable x which is the rate at the value of function changes with respect to the change of variable. Integration is a method of finding the area to the x axis from the curve.

Complete step-by-step answer:
We know the derivative is used for finding the velocity of a moving particle, when distance traversed at any time t is known. Integral is not used.
As we know velocity $=\dfrac{\text{distance}}{\text{time}}$
And we know that derivation is the rate at the value of function changes with respect to the change of variable, here
$v=\dfrac{dx}{dt}$
So, here it is clear that integration cannot be used to find the velocity of a moving object, when distance traversed at any time t is known.
So, statement I is false.
We know that the integral is used In calculating the distance traversed when the velocity at time t is known.
As we know distance $=$velocity $\times $ time.
And we know the integration is used to find the area under the curve of the function.
Here we use integration.
Distance $=\int\limits_{t1}^{t2}{v(t)dt}$
So, statement II is true that Integral is also used in calculating the distance traversed when the velocity at time t is known.
Hence, the correct option is Statement I is false; statement II is true.

Note: Don’t confuse between derivative and integral, always remember that derivative is used for a point whereas integral is never used for a point instead it is used for integral of a function over an interval.