3 years ago

What is the car's acceleration from 0 to 1 second?

Physics

1 answer:

dusya [7]3 years ago

3 0

10 mph/s because there is 60 seconds in a minute then divide by 6 which is 10.

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One side of a triangle is increasing at a rate of 5 cm/sec and a second side is increasing at a rate of 7 cm/sec. If the area of

Vanyuwa [196]

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The rate of angle is 26.25 rad/sec.

Explanation:

Given that,

First side of triangle a= 20 cm

Second side of triangle b= 50 cm

One side of a triangle is increasing at a rate = 5 cm/sec

Second side is increasing at a rate = 7 cm/s

Angle $\theta=\dfrac{\pi}{3}=60^{\circ}$

If the area of the triangle remains constant,

We need to calculate rate of angle

Using formula of area of triangle

$A=\dfrac{1}{2}ab\sin\theta$

On differentiating

$\dfrac{dA}{dt}=\dfrac{1}{2}ab\cos\theta\dfrac{d\theta}{dt}+\dfrac{1}{2}a\sin\theta\dfrac{db}{dt}+\dfrac{1}{2}b\sin\theta\dfrac{da}{dt}$

Put the value into the formula

$0=\dfrac{1}{2}\times20\times50\cos60\dfrac{d\theta}{dt}+\dfrac{1}{2}\times20\sin60\times7+\dfrac{1}{2}\times50\sin60\times5$

$\dfrac{d\theta}{dt}=\dfrac{35\sqrt{3}\times\dfrac{25}{2}\sqrt{3}\times5}{250}$

$\dfrac{d\theta}{dt}=26.25\ rad/sec$

Hence, The rate of angle is 26.25 rad/sec.

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