1-D Motion, calculating final velocity

In summary, 1-D motion refers to the movement of an object along a straight line, and final velocity is the speed and direction of an object at the end of its motion. Final velocity can be calculated using the equations v = u + at and v² = u² + 2as. In 1-D motion, speed is the rate of change of position, while velocity is the rate of change of position with direction. Acceleration directly affects final velocity, as it is the rate of change of velocity.
  • #1
mncyapntsi
38
4
Homework Statement
An electron is moving in a straight line with a velocity of 4x10^5 m/s. It enters a region 5.0 cm long where it undergoes an acceleration of
6.0x10^12 along the same straight line. (a) What is the electron’s velocity when it
emerges from this region? b) How long does the electron take to cross the region?
Relevant Equations
vf^2 = vi^2 + 2a(xf-xi)
Hello!
I have done this problem :
vf^2 = (4.0x10^5)^2 + 2(6.0x10^12)(5x10^-3)
so vf= sqrt((4.0x10^5)^2 + 2(6.0x10^12)(5x10^-3))
I get vf = 4.7 x 10^5 m/s
However, the textbook solutions says vf = 8.7x10^5 m/s.
Where did I go wrong?
Thank you for any help! :)
Screen Shot 2021-10-10 at 2.13.40 PM.png
 
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  • #2
Well... how long is a cm, again ? In terms of metres, that is.

Does that get you any closer ?
 
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  • #3
hmmm27 said:
Well... how long is a cm, again ? In terms of metres, that is.

Does that get you any closer ?
Oh no! Of course that changes the result haha.
Thank you so much for pointing that out :)
 
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FAQ: 1-D Motion, calculating final velocity

What is 1-D motion?

1-D motion refers to motion that occurs in a straight line, also known as linear motion. This means that the object is moving in only one direction along a single axis.

How do you calculate final velocity in 1-D motion?

To calculate final velocity in 1-D motion, you can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Alternatively, you can use the equation v^2 = u^2 + 2as, where s is the displacement.

What is the difference between velocity and speed in 1-D motion?

Velocity is a vector quantity that includes both magnitude (speed) and direction, while speed is a scalar quantity that only refers to the magnitude of an object's motion. In 1-D motion, velocity and speed are the same since there is only one direction of motion.

How does acceleration affect final velocity in 1-D motion?

In 1-D motion, acceleration can either increase or decrease the final velocity of an object, depending on its direction. If the acceleration is in the same direction as the initial velocity, the final velocity will increase. If the acceleration is in the opposite direction, the final velocity will decrease.

Can you calculate final velocity if the acceleration is not constant in 1-D motion?

Yes, you can still calculate final velocity if the acceleration is not constant in 1-D motion. However, you will need to use calculus to find the final velocity at a specific point in time. Alternatively, you can use the average acceleration over a specific time interval to estimate the final velocity.

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