Question

The velocity of moving object varies
with displacement ‘x’as y = 3x² – 2x, the
the acceleration at x = 2m is
1) 48ms-2 2) 80ms -2 3) 18ms -24) 10ms
-2​

Answer 1

Answer:

Explanation:

10ms-2

Answer 2

Answer:

The the acceleration at x = 2m is 80m/s².i.e.option(2)

Explanation:

The velocity of a moving object varies with displacement as,

$y=3x^2-2x$             (1)

Where,

y="velocity" of the body

x=displacement of the body

Whereas the acceleration of a body is given as the rate of change of velocity with respect to time i.e.

$a=\frac{dy}{dt}$             (2)

Whereas time is given as,

$t=\frac{dx}{y}$           (3)

By substituting the value of t in equation (2) we get;

$a=y\frac{dy}{dt}$             (4)

By substituting the value of y in equation (4) we get;

$a=(3x^2-2x)\frac{d(3x^2-2x)}{dx}=(3x^2-2x)(6x-2)$        (5)

By placing x=2m in equation (5) we get;

$a=(3(2)^2-2\times 2)(6\times 2-2)=(12-4)(12-2)=8\times 10=80m/s^2$

Hence, the the acceleration at x = 2m is 80m/s².i.e.option(2)