Kinematics-Change in speed question

[riseNshine]

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Hi everyone, this is a kinematics question from Kaplan:

At a place where g is 9.8 m/s2, an object is thrown vertically downward with a speed of 10 m/2 while a different object is thrown vertically upward with a speed of 20 m/2. What object undergoes a greater change in speed in a time of 2 seconds.

I understand the answer is that both have the same change in speed since the acceleration is constant for both cases, but I was trying to think of this in terms of numerical equations and was having difficulty working it out.

To calculate change in speed, I used the v=initial v + at equation to find the final v and then subtracted final v from initial v but that results in a different change in speed for the two scenarios.

I'm thinking there's something wrong with my thought process for the equation, can someone explain this with equations?

Thanks

 

[indianjatt]

For the downward path, we will use the equation v final = v i + at.
vf = 10 + (10)*2 = 30 m/s. Therefore the change in velocity/speed will be v final - v initial = 30-10= 20 m/s

For the upward path, we will do the same thing:
vf = 20 m/s + (-10)*2s = 0 m/s
change in speed (just magnitude of change) = 0 m/s - 20 m/s = 20 m/s

 

[milski]

That's all correct. The only part that bothers me that is actually a change in velocity, not speed. Strictly speaking, speed is non-directional and always positive. It works out ok in this question since the answer is the same for both change in velocity and change of speed but if the question was asking about a longer time period, say 4 second, the change in speed would not be the same for the two objects even though the acceleration is the same.

 

[sciencebooks]

That's all correct. The only part that bothers me that is actually a change in velocity, not speed. Strictly speaking, speed is non-directional and always positive. It works out ok in this question since the answer is the same for both change in velocity and change of speed but if the question was asking about a longer time period, say 4 second, the change in speed would not be the same for the two objects even though the acceleration is the same.

I totally thought of the same thing with the directions... Because technically, the change in velocity of the one doing up is 0-20=-20 so the changes are different because different signs. Usually they're careful to say something like "magnitude of velocity" but I've noticed that sometimes, they just use "speed" when really they're different things and it could really mess up answering, especially if the answer choices were conceptual.

And then like you said, with the time, it'd be different, because the one doing down would keep on accelerating and increasing it's velocity, but the one going up would have come to momentary zero velocity at the top and then have to "start" gaining velocity from zero.