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3 years ago

It takes 180 kj of work to accelerate a car from 21.0 m/s to 27.0 m/s. what is the car's mass?

Physics

1 answer:

beks73 [17]3 years ago

4 0

558888544446556313321

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a bus is moving with the velociity of 36 km/hr . after seeing a boy at 20 m ahead on the road, the driver applies the brake and

Klio2033 [76]

Answer:

Assumption: the acceleration of this bus is constant while the brake was applied.

Acceleration of this bus: approximately $\left(-6.0\; \rm m \cdot s^{-2}\right)$ .

It took the bus approximately $1.7\;\rm s$ to come to a stop.

Explanation:

Quantities:

Displacement of the bus: $x = 10\; \rm m$ .
Initial velocity of the bus: $\displaystyle u = 36\; \rm km \cdot hr^{-1} = 36\; \rm km \cdot hr^{-1}\times \frac{1\; \rm m \cdot s^{-1}}{3.6\; \rm km\cdot hr^{-1}} = 10\; \rm m \cdot s^{-1}$ .
Final velocity of the bus: $v = 0\; \rm m\cdot s^{-1}$ because the bus has come to a stop.
Acceleration, $a$ : unknown, but assumed to be a constant.
Time taken, $t$ : unknown.

Consider the following SUVAT equation:

$\displaystyle x = \frac{1}{2}\, \left(a\, t^2\right) + u\, t$ .

On the other hand, assume that the acceleration of this bus is indeed constant. Given the initial and final velocity, the time it took for the bus to stop would be inversely proportional to the acceleration of this bus. That is:

$\displaystyle t = \frac{v - u}{a}$ .

Therefore, replace the quantity $t$ with the expression $\displaystyle \left(\frac{v - u}{a}\right)$ in that SUVAT equation:

$\displaystyle x = \frac{1}{2}\, \left(a\, \left(\frac{v -u}{a}\right)^2\right) + u\, \left(\frac{v - u}{a}\right)$ .

Simplify this equation:

$\begin{aligned}x &= \frac{1}{2}\, \left(a\, {\left(\frac{v -u}{a}\right)}^2\right) + u\, \left(\frac{v - u}{a}\right) \\ &= \frac{1}{2}\left(\frac{{(v - u)}^2}{a}\right) + \frac{u\, (v - u)}{a} =\frac{1}{a}\, \left(\frac{{(v - u)}^2}{2} + u\, (v - u)\right)\end{aligned}$ .

Therefore, $\displaystyle a= \frac{1}{x}\, \left(\frac{{(v - u)}^2}{2} + u\, (v - u)\right)$ .

In this question, the value of $x$ , $u$ , and $v$ are already known:

$x = 10\; \rm m$ .
$\displaystyle u =10\; \rm m \cdot s^{-1}$ .
$v = 0\; \rm m\cdot s^{-1}$ .

Substitute these quantities into this equation to find the value of $a$ :

$\begin{aligned} a &= \frac{1}{x}\, \left(\frac{{(v - u)}^2}{2} + u\, (v - u)\right) \\ &= \frac{1}{10\; \rm m}\times \left(\frac{{\left(0\; \rm m \cdot s^{-1} - 10\; \rm m \cdot s^{-1}\right)}^2}{2} + \left(0\; \rm m \cdot s^{-1} - 10\; \rm m \cdot s^{-1}\right)\times 10\; \rm m \cdot s^{-1}\right)\\ &\approx -6.0\; \rm m \cdot s^{-2}\end{aligned}$ .

(The value of acceleration $a$ is less than zero because the velocity of the bus was getting smaller.)

Substitute $a \approx -6.0\; \rm m \cdot s^{-2}$ (alongside $u = 10\; \rm m \cdot s^{-1}$ and $v = 0\; \rm m \cdot s^{-1}$ ) to estimate the time required for the bus to come to a stop:

$\begin{aligned}t &= \frac{v - u}{a} \\ &\approx \frac{0\; \rm m \cdot s^{-1} - 10\; \rm m \cdot s^{-1}}{-6.0\; \rm m \cdot s^{-2}} \approx 1.7\; \rm s\end{aligned}$ .

8 0

3 years ago

Tarzan swings on a 35.0 m long vine initially inclined at an angle of 44.0◦ with the vertical. The acceleration of gravity if 9.

maks197457 [2]

Answer:

(A) Vf = 13.8 m/s

(B) Vf = 15.1 m/s

Explanation:

length of rope (L) = 35 m

angle to the vertical = 44 degrees

acceleration due to gravity (g) = 9.8 m/s^{2}

(A) from conservation of energy

final kinetic energy + final potential energy = initial kinetic energy + initial potential energy

0.5m(Vf)^{2} + mg(Hf) = 0.5m(Vi)^{2} + mg(Hi)

where

m = mass

Hi = initial height = 35 cos 44 = 25.17

Hf = final height = length of vine = 35 m

Vi = initial velocity = 0 since he starts from rest

Vf = final velocity

the equation now becomes

0.5m(Vf)^{2} + mg(Hf) = mg(Hi)

0.5m(Vf)^{2} = mg (Hi - Hf)

0.5(Vf)^{2} = g (Hi - Hf)

0.5(Vf)^{2} = 9.8 x (25.17 - 35)

0.5(Vf)^{2} = - 96.3 (the negative sign tells us the direction of motion is downwards)

Vf = 13.8 m/s

(B) when the initial velocity is 6 m/s the equation remains

0.5m(Vf)^{2} + mg(Hf) = 0.5m(Vi)^{2} + mg(Hi)

m(0.5(Vf)^{2} + g(Hf)) = m(0.5(Vi)^{2} + g(Hi))

0.5(Vf)^{2} + g(Hf) = 0.5(Vi)^{2} + g(Hi)

0.5(Vf)^{2} = 0.5(Vi)^{2} + g(Hi) - g(Hf)

0.5(Vf)^{2} = 0.5(6)^{2} + (9.8 x (25.17 - 35))

0.5(Vf)^{2} = -114.3 ( just as above, the negative sign tells us the direction of motion is downwards)

Vf = 15.1 m/s

5 0

3 years ago

Read 2 more answers

How is heat related to phase changes

bekas [8.4K]

The heat is used to break the bonds between the ice molecules as they turn into a liquid phase. Since the average kinetic energy of the molecules does not change at the moment of melting, the temperature of the molecules does not change.

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3 years ago

Which of these items would be a renewable resource?

Irina18 [472]

Trees can be a renewable source , we use them to breath , we make paper out of them , we make houses and etc.

i hope this helps

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3 years ago

A .025 kg bullet is moving at 350 m/s when it hits and then passes through a 7 kg block of wood. After the bullet passes through

slamgirl [31]

Answer:

The final velocity of the wooden block is equal to $1.035 m/s$