Question

29. A train travelling at 20 m s-accelerates at 0.5 m -2 for 30 s. How far will it travel in this time?
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Answer 1

$\sf{\large{\underline{\underline{EXPLANATION:}}}}$

$\sf{Given}\begin{cases}\sf{u=20ms^{-1}}\\ \sf{a=0.5ms^{-2}}\\ \sf{t=30}\end{cases}$

★To find:

• Distance s travelled by the body in 30s.

★Using 2nd equation of motion,,

s=ut+½at²

$\sf</strong><strong>{</strong><strong>\</strong><strong>i</strong><strong>m</strong><strong>p</strong><strong>l</strong><strong>i</strong><strong>e</strong><strong>s</strong><strong>{</strong><strong>s</strong><strong>=</strong><strong>2</strong><strong>0</strong><strong>t</strong><strong>\</strong><strong>f</strong><strong>r</strong><strong>a</strong><strong>c</strong><strong>{</strong><strong>1</strong><strong>}</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong>\</strong><strong>t</strong><strong>i</strong><strong>m</strong><strong>e</strong><strong>s</strong><strong>{</strong><strong>0</strong><strong>.</strong><strong>5</strong><strong>}</strong><strong>\</strong><strong>t</strong><strong>i</strong><strong>m</strong><strong>e</strong><strong>s</strong><strong>{</strong><strong>t</strong><strong>^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong>}</strong><strong>}</strong><strong>}$

$\sf{\implies{s=20t+</strong><strong>\</strong><strong>f</strong><strong>r</strong><strong>a</strong><strong>c</strong><strong>{</strong><strong>1</strong><strong>t</strong><strong>^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong>}</strong><strong>{</strong><strong>4</strong><strong>}</strong><strong>}}$

$\sf{\implies{s=\frac{</strong><strong>8</strong><strong>0</strong><strong>t</strong><strong>+</strong><strong>1t</strong><strong>^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong>}{4}}}$

$\sf{\implies{s=\frac{80</strong><strong>(</strong><strong>3</strong><strong>0</strong><strong>)</strong><strong>+</strong><strong>1</strong><strong>(</strong><strong>3</strong><strong>0</strong><strong>)</strong><strong>^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong>}{4}}}$

$\sf{\implies{s=\frac{</strong><strong>2</strong><strong>4</strong><strong>0</strong><strong>0</strong><strong>+</strong><strong>9</strong><strong>0</strong><strong>0</strong><strong>}{4}}}$

$\sf{\implies{s=</strong><strong>\</strong><strong>c</strong><strong>a</strong><strong>n</strong><strong>c</strong><strong>e</strong><strong>l</strong><strong>\</strong><strong>d</strong><strong>frac{</strong><strong>3</strong><strong>3</strong><strong>0</strong><strong>0</strong><strong>}{4}}}$

$\sf{\implies{s=</strong><strong>8</strong><strong>2</strong><strong>5</strong><strong>m</strong><strong>}}$

Therefore,,

Distance s travelled by the body = 825m

$\rule{200}2$

❣️❣️★Hope it helps★❣️❣️