Was the Particle's Acceleration Ever 4 During Its Journey?

[singedang2]

Homework Statement

A particle travels a unit distance in a unit amount of time. It starts at rest and ends at rest.

I need to show that, at some time during the trip, the magnitude of the particle’s
acceleration was at least 4.

Homework Equations

The Attempt at a Solution

i really don't know how to do this problem. any hints?

 

[singedang2]

help pls. thanks!

 

[Doc Al]

Hint: Imagine the particle accelerating uniformly for the first half of the distance, then decelerating uniformly during the second half.

 

[singedang2]

so how am i supposed to show that? a/2 + (-a/2) = ??/

 

[Doc Al]

Given my hint, what acceleration does it imply? Use your knowledge of kinematics to relate distance, time, and acceleration.

 

[singedang2]

so you're saying i need to show that while it was accelerating for the first half, the magnitude was 4?
and i don't clearly get what it means to travel unit distance in a unit amount of time. isn't unit normally mean 1?

 

[Doc Al]

so you're saying i need to show that while it was accelerating for the first half, the magnitude was 4?

Right. That's the gentlest way to accelerate and will give you the minimum acceleration.

and i don't clearly get what it means to travel unit distance in a unit amount of time. isn't unit normally mean 1?

Sure, what's the problem? Distance = 1 unit. (That unit distance could a meter, a foot, 25.3 miles, whatever... doesn't matter! Call it 1 distance unit.)

Same for time.

Whatever the unit is, speed is measured in Distance Units/Time units; acceleration will be in Distance units/Time units squared.

 

[tim_lou]

Cut the distance interval in half. show that at least one of the interval takes less than 1/2 a minute to travel through. Then show that in that interval, the average velocity must be at least some value. Then, using the mean value theorem, at some point in the interval, the speed must be that value. use similar arguments to show that the acceleration must be at least some value (namely 4) in some interval.