A car travels 43 km in 56 minutes.

Mathematics

1 answer:

patriot [66]3 years ago

6 0

Answer:

$\displaystyle v=46.07\ Km/h$

Step-by-step explanation:

Speed

The speed is the ratio between the distance x traveled by an object and the time t taken.

$\displaystyle v=\frac{x}{t}$

The car travels x=43 Km in t=56 minutes. We are required to express the speed in Km/h. The time needs to be expressed in hours:

$t = 56 / 60 = 0.933\ h$

Now apply the formula:

$\boxed{\displaystyle v=\frac{43}{0.933}=46.07\ Km/h}$

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As a motorcycle accelerates at 5.1 m/s2, its speed changes from 16 km/h to 118 km/h. How long does this take?

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Acceleration (a) = 5.1 m/s²
Initial speed (u) = 16 km/h ⇒ $\frac{16*1000}{3600}$ m/s ≈ 4.5m/s
Final speed (v) =118 km/h ⇒ $\frac{118*1000}{3600}$ m/s ≈ 32.8m/s

Distance(S) travel in that particular instant is carried out by 'Third equation of motion' i.e., v² = u² + 2aS

So, When all quantities are in S.I. unit then,
putting the values in the equation of motion,

As we have to carry out the distance covered,
2·a·S = v² - u²
S = $\frac{ v^{2} - u^{2} }{2a}$
Putting values in derived equation,
⇒ S = $\frac{ (32.8)^{2} - (4.5)^{2} }{2*(5.1)}$
⇒ S = $\frac{ 1075.84 - 20.25}{10.2}$
⇒ S = $\frac{1055.59}{10.2}$
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The total distance covered in that given condition is approx. 103.289 m.

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