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3 years ago

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A car is brought to rest in a distance of 484m using a constant acceleration of -8.0m/s^2. What was the velocity of the car when

the acceleration first began?

1 answer:

Agata [3.3K]3 years ago

6 0

Answer:

88 m/s

Explanation:

To solve the problem, we can use the following SUVAT equation:

$v^2-u^2=2ad$

where

v is the final velocity

u is the initial velocity

a is the acceleration

d is the distance covered

For the car in this problem, we have

d = 484 m is the stopping distance

v = 0 is the final velocity

$a=-8.0 m/s^2$ is the acceleration

Solving for u, we find the initial velocity:

$u=\sqrt{v^2-2ad}=\sqrt{-2(8.0)(484)}=88 m/s$

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Answer:

(a) $v_f=0.5\frac{m}{s}$

(b) $v_f=-11\frac{m}{s}$

Explanation:

(a) Since a constant external force is applied to the body, it is under an uniformly accelerated motion. Using the following kinematic equation, we calculate the final velocity of the mass if it is initially at rest( $v_0=0$ ):

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According to Newton's second law:

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Replacing (2) in (1):

$v_f=\frac{F}{m}t\\v_f=\frac{2.5N}{4.5kg}(0.9s)\\v_f=0.5\frac{m}{s}$

(b) In this case we have $v_0=-11.5\frac{m}{s}$ . So, we use the final velocity equation:

$v_f=v_0+at\\v_f=v_0+\frac{F}{m}t\\v_f=-11.5\frac{m}{s}+\frac{2.5N}{4.5kg}(0.9s)\\v_f=-11\frac{m}{s}$

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2 years ago

A copper rod 81 cm long is used to poke a fire. the hot end of the rod is maintained at 105° c and the cool end has a constant t

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The temperature inside the copper rod varies linearly with the distance from the hot end of the rod. This means that we can find the temperature at 23 cm (let's call it 'point A') from the cool end by solving a linear proportion.

The temperature difference between the two ends of the rod is
$\Delta T = 105^{\circ}-21^{\circ} = 84^{\circ}$
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from which we find
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This is not the final answer actually; this is the temperature difference between the cool end and point A. So, the temperature at point A is
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⦁ A certain resistor is required to dissipate 0.25 W, what standard rating should be used?

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Explanation:

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A 40.0-mH inductor is connected to a North American electrical outlet (ΔVrms = 120 V, f = 60.0 Hz). Assuming the energy stored i

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Explanation:

It is given that,

Inductance, $L=40\ mH=40\times 10^{-3}\ H$

RMS value of voltage, $v_{rms}=120\ V$

Frequency, f = 60 Hz

We need to find the energy stored at t = (1 /185) s. It is assumed that energy stored in the inductor is zero at t = 0. So,

The current flowing through the inductor is given by :

$I_t=\dfrac{V_o}{X_L}\ (sin\ \omega t-\dfrac{\pi}{2})$

$I_t=\dfrac{\sqrt{2} V_{rms}}{X_L}\ (sin\ \omega t-\dfrac{\pi}{2})$

$I_t=\dfrac{120\sqrt{2}}{2\pi f L}\ sin(2\pi f t-\dfrac{\pi}{2})$

$I_t=\dfrac{120\sqrt{2}}{2\pi\times 60\times 40\times 10^{-3}}\ sin(2\pi \times 60\times \dfrac{1}{185})-\dfrac{\pi}{2})$

$I_t=\dfrac{120\sqrt2}{15.07}\ sin(2\pi \times 60\times \dfrac{1}{185}-\dfrac{\pi}{2})$

I = 0.091 A

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$U=\dfrac{1}{2}\times 40\times 10^{-3}\times (0.091)^2$

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Hence, this is the required solution.

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3 years ago

A compact car, mass 660 kg, is moving at 1.00 ✕ 102 km/h toward the east. The driver of the compact car suddenly applies the bra

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Answer: $59.43\times 10^3 kg-m/s$

Explanation:

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mass of car $m=660 kg$

Initial velocity of car $=102 km/h\approx 28.33 m/s$ towards east

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Force exerted $F_{avg}=4.8\times 10^3 N$

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$Impulse(J)=-F\cdot t$

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$J=-59.49\times 10^3 kg-m/s$

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