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# Formula of question

+3
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I don't understand the Formula  of this question

xvxvxv  Sep 26, 2014

#2
+91919
+8

Let the distance travelled in the fist 5 seconds be x metres

We know u=0

When t=5, s=x

When t=10 s=x+150

I am going to use the formula     $${\mathtt{s}} = {\mathtt{ut}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{{\mathtt{at}}}^{{\mathtt{2}}}$$

since u=0,  the formula becomes  $${\mathtt{s}} = {\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{{\mathtt{at}}}^{{\mathtt{2}}}$$

Now we have 2 equations that can be solved simultaneously.

$$\\x=\frac{1}{2}a\times 5^2 \\\\\ x= \frac{1}{2}a\times 25 \qquad (1)\\\\ and\\\\ x+150=\frac{1}{2}a\times 10^2 \\\\ x+150=\frac{1}{2}a\times 100 \\\\ x+150=\frac{1}{2}a\times 25 \times 4 \\\\ \frac{x+150}{4}=\frac{1}{2}a\times 25 \qquad (2)\\\\ putting these together I get\\\\ \begin{array}{rll} x&=&\frac{x+150}{4}\\ 4x&=&x+150\\ 3x&=&150\\ x&=&50\\ \end{array}$$

So the ball rolls 50m in the first 5 seconds

Melody  Sep 27, 2014
Sort:

#1
+8256
0

Is the s after the 5.0 seconds?

DragonSlayer554  Sep 26, 2014
#2
+91919
+8

Let the distance travelled in the fist 5 seconds be x metres

We know u=0

When t=5, s=x

When t=10 s=x+150

I am going to use the formula     $${\mathtt{s}} = {\mathtt{ut}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{{\mathtt{at}}}^{{\mathtt{2}}}$$

since u=0,  the formula becomes  $${\mathtt{s}} = {\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{{\mathtt{at}}}^{{\mathtt{2}}}$$

Now we have 2 equations that can be solved simultaneously.

$$\\x=\frac{1}{2}a\times 5^2 \\\\\ x= \frac{1}{2}a\times 25 \qquad (1)\\\\ and\\\\ x+150=\frac{1}{2}a\times 10^2 \\\\ x+150=\frac{1}{2}a\times 100 \\\\ x+150=\frac{1}{2}a\times 25 \times 4 \\\\ \frac{x+150}{4}=\frac{1}{2}a\times 25 \qquad (2)\\\\ putting these together I get\\\\ \begin{array}{rll} x&=&\frac{x+150}{4}\\ 4x&=&x+150\\ 3x&=&150\\ x&=&50\\ \end{array}$$

So the ball rolls 50m in the first 5 seconds

Melody  Sep 27, 2014

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