Question

The displacement of a body in t seconds is given by x=3+2t+1/2t^2 in meter. Its acceleration is ​

Answer 1

given ,

$x = 3 + 2t + \frac{1}{2} t {}^{2}$

we know that

v = dx / dt = 2+ t

and

dv/ dt = a = 1m / s

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Answer 2

The acceleration of the body is found to be $1 \mathrm{~m} / \mathrm{s}^{2}$.

Given:

The displacement of a body in t seconds is given by the equation

$\mathrm{X}=3+2 \mathrm{t}+1/2\mathrm{t}^{2}$

where, t is taken is sec.

Explanation:

To determine the value of velocity, differentiate the equation of  displacement 'x' with respect to time t.

$\begin{aligned}&x=3+2 t+1/2 t^{2} \\&v=\frac{d x}{d t}=0+2+1 t\end{aligned}$

Again differentiating the velocity to get the value of acceleration,

$a={d v}/{d t} = 0+0+1 \end{aligned}$

Hence, the acceleration of the body for the given displacement is $1 \mathrm{~m} / \mathrm{s}^{2}$.

To know more about differentiation, here

https://brainly.in/question/1238773?msp_poc_exp=2

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