Question

A particle moves along x-axis in such a w
its x-co-ordinate varies with time according to the
equation X = 4 - 2t + t^2 . The speed of the particle
will vary with time as

4 graphs are given in attachment ​

Answer 1

SOLUTION.

Here I use my some differential knowledge as well as knowledge of straight line. let's see....

X = 4 - 2t + t²

Differentiate the EQUATION with respect to time.

dX/dt = 0 - 2 +2t

we know that is differential equations we write dx/dt as velocity

v = 2t - 2

Form of writing a straight line.

If a line with angle © with the X axis in anticlockwise sense and make intercept of c on y axis. Than such line can be represented as...

Y = [tan©]X + c

where tan© known as slope of the line

Now we interpret our EQUATION derived above..

v = 2t - 2

here the slope of the line is 2 hence angleade by the line with X axis is less than 90° because tan operator is positive in first quadrant i.e from 0 to 90.

The intercept is -2 hence it intercept with negative y axis.

So from these two points the answer is....

OPTION B

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