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Effectus [21]
3 years ago
15

Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 3t^2 + cos(t) and v(0) = 2.

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
6 0
\bf \displaystyle a(t)=3t^2+cos(t)\implies \stackrel{velocity}{\int~ [3t^2+cos(t)]dt}\\\\\\ t^3+sin(t)+C=~~~v(t)
\\\\\\
\begin{cases}
v(0)=2\\
v=2\\
t=0
\end{cases}\implies 0^3+sin(0)+C=2\implies C=2
\\\\\\
\boxed{t^3+sin(t)+2=v(t)}
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Approximately how many times greater is 1.2×103 than 4×10−1 ?
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Let your calculator do the work. Be careful how you enter this in. (Are you supposed to estimate it? We'll get around to that.) Write it like this.

1.2 * 10^3 divided by 4 * 10^-1 Your calculator will do this nicely. The trick is the - 1. Put it in the calculator like this.
1.2 
*
10
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That's one way to do it. Another way is just to do it all by hand. The numbers are easy enough
1.2 * 10^3 means shift the decimal 3 places right. 1 200 which is 1200
4 * 10^-1 can be handled 2 ways 10 to the minus 1 in the denominator becomes 10^1 in the numerator. Notice the sign change on the 10 when you shift if :it becomes plus! That's why you did it.

1200 * 10^1 
12000

Now you are still left with 4 in the denominator.
12000/4 = 3000. 

The first method always works. The second one gives you a better understanding of how powers work. There are other ways of doing this, but these are the two best, I think.
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