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  • $a=4$

  • ${\bf R}(t)=7\sin(at)\hat{{\bf x}}+4e^{-8t}\hat{{\bf y}}+8t^{3}\hat{{\bf z}}$

how do I find the acceleration at time $t = 0.27778$

I know that the third derivative is: $ \vec {R^{(3)}(t)} = -7a^3\cos(at)\hat x -2048e^{-8t}\hat y +48\hat z$

Now, how do I take it from here? and how do I calculate it?

Firas Abd El Gani
  • 2,136

2 Answers2

1

If $R(t)$ is the position vector at time $t$, then $R'(t)$ is the velocity vector at time $t$ and $R''(t)$ is the acceleration vector at time $t$. Here the derivatives are taken component-wise.

The third derivative $R^{(3)}(t)$ is sometimes called jerk, as I recall.

MPW
  • 43,638
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The acceleration is the second derivative of the position vector, not the third.

Just find $\overrightarrow {{R^{(2)}}(t)}$ then substitute $t=0.27778$.

Rory Daulton
  • 32,288
  • thats it that i don't know how to take final number from substituting in : $"\vec {R''(t)} = -7a^2\sin(at)\hat x +256e^{-8t}\hat y +48t\hat z"$ while having x,y,z. – Firas Abd El Gani Nov 08 '14 at 13:30
  • @FirasAliAbdelGhani: Just use $a=4$ and $t=0.27778$. So use your calculator to enter $-74^2sin(4*0.27778)$ and that is the $\hat x$ component, and similarly for the other components. Many calculators let you assign the values of $a$ and $t$ and that would be easier and less error-prone. – Rory Daulton Nov 08 '14 at 13:34
  • so Im not supposed to get a final number? im not supposed to do a module of all components? – Firas Abd El Gani Nov 08 '14 at 13:37
  • IT worked ! thanks! – Firas Abd El Gani Nov 08 '14 at 13:39
  • @FirasAliAbdelGhani: Note that it's a vector, not a number – MPW Nov 08 '14 at 13:57