Question

The distance x covered by a body moving in a straight line in time t is given by x2 = t2 + 2t + 3. The
acceleration of the body will vary as:
A)
B)
2
C)
3
D)
4
X​

Answer 1

Given that,

The distance x covered by a body moving in a straight line in time t is given by :

$x^2=t^2+2t+3$ ......(1)

To find,

Acceleration of the body varies as?

Solution,

Acceleration of the body is given by :

$a=\dfrac{d^2x}{dt^2}$

Differentiating equation (1) wrt t such that :

$\dfrac{d(x^2)}{dt}}=\dfrac{d(t^2+2t+3)}{dt}\\\\2x\dfrac{dx}{dt}=2t+2$ .....(2)

Since, $v=\dfrac{dx}{dt}$

Now, differentiating equation (2) wrt t we get :

$2(x\dfrac{d^2x}{dt^2}+\dfrac{dx}{dt})=2\\\\(x\dfrac{d^2x}{dt^2}+\dfrac{dx}{dt})=1\\\\xa+v=2\\\\a=\dfrac{2-v}{x}\\\\a\propto x^{-1}$

Thus, this is the required solution.

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