Question

The brakes of a car whose initial velocity is 30 m/s are applied, and the car receives an acceleration of -2.1 m/s 2 . How far will it have gone?
(a) when its velocity has decreased to 15 m/s, and
(b) When it has come to a stop?

Answer 1

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

$\textbf{\underline{\underline{Case 1}}}</p><p>$

★Given,,

• Initial velocity of the car,u=30m/s

• Final velocity of the car,v=15m/s

• Acceleration,a=-2.1m/s²

★To find,,

• Distance covered by the car,s=??

★Using 3rd equation of motion,,

$\mathtt{\</strong><strong>b</strong><strong>o</strong><strong>x</strong><strong>e</strong><strong>d</strong><strong>{</strong><strong>v^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong>-u^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong>=</strong><strong>2</strong><strong>a</strong><strong>s</strong><strong>}}$

$</strong><strong>\</strong><strong>s</strong><strong>f</strong><strong>{</strong><strong>\</strong><strong>i</strong><strong>m</strong><strong>p</strong><strong>l</strong><strong>i</strong><strong>e</strong><strong>s</strong><strong>{</strong><strong>1</strong><strong>5</strong><strong>^{2}-</strong><strong>3</strong><strong>0</strong><strong>^{2}=2</strong><strong>(</strong><strong>-</strong><strong>2</strong><strong>.</strong><strong>1</strong><strong>)</strong><strong>s</strong><strong>}}$

$\sf{\implies{</strong><strong>2</strong><strong>2</strong><strong>5</strong><strong>-</strong><strong>9</strong><strong>0</strong><strong>0</strong><strong>=</strong><strong>-</strong><strong>4</strong><strong>.</strong><strong>2</strong><strong>s}}$

$\sf{\implies{</strong><strong>\</strong><strong>f</strong><strong>r</strong><strong>a</strong><strong>c</strong><strong>{</strong><strong>-</strong><strong>6</strong><strong>7</strong><strong>5</strong><strong>}</strong><strong>{</strong><strong>-</strong><strong>4</strong><strong>.</strong><strong>2</strong><strong>}</strong><strong>=s}}$

$\sf{\implies{</strong><strong>s</strong><strong>=</strong><strong>1</strong><strong>6</strong><strong>0</strong><strong>.</strong><strong>7</strong><strong>m</strong><strong>}}$

★Therefore,,

The car covered 160.7m

$\rule{200}2$

$\textbf{\underline{\underline{Case 2}}}</p><p>$

★Given,,

• Initial velocity of the car,u=30m/s

• Final velocity of the car,v=0m/s

• Acceleration,a=-2.1m/s²

★To find,,

• Distance covered by the car,s=??

★Using 3rd equation of motion,,

$\mathtt{\boxed{0^{2}-30^{2}=2as}}$

$\sf{\implies{0-900=2(-2.1)s}}$

$\sf{\implies{-900=-4.2s}}$

$\sf{\implies{\frac{9000}{42}=s}}$

$\sf{\implies{s=214.2m}}$

$\rule{200}2$

Hope it helps ❣️❣️❣️