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3 years ago

6

A car is driving 25.5 m/s when it hits

1 answer:

IceJOKER [234]3 years ago

6 0

Answer:

it takes the car 4.362 seconds to cover the distance of 88.4 m.

Explanation:

The distance the car covers is given by the function

$x(t) = vt-\dfrac{1}{2}at^2$ ,

where $v = 25.5m/s$ , and $a = 2.40m/s$ , putting these in we get:

$x(t) = 25.5t-\dfrac{1}{2}(2.4)t^2\\\\x(t) = 25.5t-1.2t^2$

Now, when the car has moved to 88.4m, $x(t) = 88.4$ , or

$x(t) = 25.5t-1.2t^2 = 88.4$

which is a quadratic equation with solutions

$t = 4.362s,\\t = 16.887s$

We take the first solution $t = 4.362s$ , <em>since at that time the car is still moving right and decelerating</em>. The second solution $t =16.887$ describes the situation where the car has stopped decelerating and is now moving leftwards because the decelerating is leftwards, <em>which is utterly wrong because we know that cars do not start moving backwards after the brakes have stopped them! </em>

Thus, it takes the car 4.362 seconds to cover the distance of 88.4 m.

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Read 2 more answers

a sphere of diameter 6•0cm is moulded into a thin uniform wire of diameter 0•2mm.calculate the length of the wire in metres

Scilla [17]

The length of the wire is 36 m.

<u>Explanation:</u>

Given, Diameter of sphere = 6 cm

We know that, radius can be found by taking the half in the diameter value. So,

$\text { sphere radius, } R=\frac{D}{2}=\frac{6}{2}=3 \mathrm{cm}=3 \times 10^{-2} \mathrm{m}$

Similarly,

$\text { wire radius, } r=\frac{0.2}{2}=0.1 \mathrm{mm}=1 \times 10^{-3} \mathrm{m}$

We know the below formulas,

$\text {volume of sphere}=\frac{4}{3} \times \pi \times R^{3}$

$\text {volume of wire}=\pi \times r^{2} \times l$

When equating both the equations, we can find length of wire as below, where $\pi=\frac{22}{7}$

$\frac{4}{3} \times \pi \times R^{3}=\pi \times r^{2} \times l$

$\frac{4}{3} \times \frac{22}{7} \times\left(3 \times 10^{-2}\right)^{3}=\frac{22}{7} \times\left(1 \times 10^{-3}\right)^{2} \times l$

The $\pi$ value gets cancelled as common on both sides, we get

$\frac{4}{3} \times 27 \times 10^{-6}=10^{-6} \times l$

The $10^{-6}$ value gets cancelled as common on both sides, we get

$l=4 \times 9=36 m$

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3 years ago