Question

The displacement of the particle along a straight line at time t is given by x=a0 +a1t +a2t^2 where a0 , a1 and a2 are constants. the acceleration of the particle is ?

Answer 1

hope this would help you.

Answer 2

The position x of a particle moving along a straight line at any instant is given by

$x=a_0+a_1t+a_2t^2$

Its acceleration is $\boxed{2a_2}$

Explanation:

Given

The position x of a particle moving along a straight line

$x=a_0+a_1t+a_2t^2$

We know that rate of change of position is velocity

i.e. $v=\frac{dx}{dt}$

And, rate of change of velocity is acceleration

i.e. $a=\frac{dv}{dt}$

Therefore,

The velocity function is given by

$v=\frac{dx}{dt}$

$\implies v=a_1+2a_2t$

And the acceleration is given by

$a=\frac{dv}{dt}$

$\implies a=2a_2$

Hope this answer is helpful.

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