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1 year ago

Two objects moving with the same speed may not have the same velocity. Why?

1 answer:

Nutka1998 [239]1 year ago

4 0

Objects have the same velocity only if they are moving at the same speed and in the same direction. Objects moving at different speeds, in different directions, or both have different velocities.

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If position vector r = bt^2i + ct^3j, where b and c are positive constants, when does the velocity vector make an angle of 450 w

vazorg [7]

$\vec r(t)=bt^2\,\vec\imath+ct^3\,\vec\jmath$

The velocity at time $t$ is

$\dfrac{\mathrm d\vec r(t)}{\mathrm dt}=2bt\,\vec\imath+3ct^2\,\vec\jmath$

Take two vectors that point in the positive $x$ and positive $y$ directions, such as $\vec\imath$ and $\vec\jmath$ . The dot products of the velocity vector with $\vec\imath$ and $\vec\jmath$ are

$\dfrac{\mathrm d\vec r(t)}{\mathrm dt}\cdot\vec\imath=2bt=\sqrt{4b^2t^2+9c^2t^4}\cos\theta$

and

$\dfrac{\mathrm d\vec r(t)}{\mathrm dt}\cdot\vec\jmath=3ct^2=\sqrt{4b^2t^2+9c^2t^4}\cos\theta$

We want the angles between these vectors to be 45º, for which we have $\cos45^\circ=\frac1{\sqrt2}$ . So

$\begin{cases}2\sqrt2\,bt=\sqrt{4b^2t^2+9c^2t^4}\\3\sqrt2\,ct^2=\sqrt{4b^2t^2+9c^2t^4}\end{cases}\implies3\sqrt2\,ct^2-2\sqrt2\,bt=0$

$\implies t(3ct-2b)=0$

$\implies t=0\text{ or }t=\dfrac{2b}{3c}$

When $t=0$ , the velocity vector is equal to the zero vector, which technically has no direction/doesn't make an angle with any other vector. So the only time this happens is for

$\boxed{t=\dfrac{2b}{3c}}$

7 0

3 years ago

Is there any change in the pressure of container filled with water when the volumed is increased

marshall27 [118]

Not really the volume of a container is simply length X width X depth so just how big the container unless the water is pressurized by some sort of weight or if the containers air pressure is lowered

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3 years ago

If there is no friction in a rollercoaster is the speed the same throughout?

andrey2020 [161]

If there is no friction, the roller coaster would keep moving forever but a constant velocity. The only way it would accelerate is if there was a force continually pushing on it.

4 0

3 years ago

Read 2 more answers

Marcia dropped a ball from a height of 20 meters and let it bounce once. As the ball is dropped, energy is transferred between p

kodGreya [7K]

Answer:

if the balls drop potential energy turns into kinetic energy

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4 years ago

the velocity of a car traveling in the positive direction decreases from 32 m/s to 24 m/s in 4 seconds. what is the average acce

anastassius [24]

Answer:

$a=-2m/sec^2$

Negative sign shows that velocity of the car is decreases at a constant rate

Explanation:

We have given velocity of the car is decreases from 32 m /sec to 24 m/sec in 4 second

So initial velocity of the car u = 32 m /sec

And finally car reaches to a velocity of 24 m/sec

Time taken to change in velocity = 4 sec

So final velocity v = 24 m/sec

From first equation of motion v = u+at

So $24=32+a\times 4$

$a=-2m/sec^2$

Negative sign shows that velocity of the car is decreases at a constant rate

6 0

3 years ago

Two objects moving with the same speed may not have the same velocity. Why?​

Two objects moving with the same speed may not have the same velocity. Why?