Mathematics (1 Viewer)

spotspot1 · Jun 13, 2016

Can someone help me with this question?

A particle has a constant acceleration of 12ms^(-2).
If the particle has a velocity of 2 ms^(-1) and
3m from the origin after 5s, find its displacement after 10 seconds.

The answer is 163m

InteGrand · Jun 13, 2016

spotspot1 said:
Can someone help me with this question?

A particle has a constant acceleration of 12ms^(-2).
If the particle has a velocity of 2 ms^(-1) and
3m from the origin after 5s, find its displacement after 10 seconds.

The answer is 163m

$\noindent Let its displacement at time $t$ (measured in seconds) be $x\equiv x(t)$ (measured in metres), so we are given $\ddot{x}=12$ (constant). Then integrating yields $\dot{x}=c_1 + 12t$ for some constant $c_1$. When $t=5$, $\dot{x}=2$, so $2=c_1 + 60 \Rightarrow c_1 = -58$. Thus $\dot{x} = -58 + 12t$. Hence another integration yields $x = c_2 -58t + 6t^2$ for some constant $c_2$. When $t=5$, $x=3$, so $3=c_2 - 58\times 5 + 6\times 5^2 \Rightarrow c_2 = 3 + 290 -150 = 143$. Thus $x(t) = 143-58t + 6t^2$. When $t=10$, we have $x=143-580+600=163$.$

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Mathematics (1 Viewer)

spotspot1

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InteGrand

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