Calculating Total Distance For Motion Questions (1 Viewer)

[AsuTeksu]

Hi all, it's me again...

Is there a general rule for calculating the total distance travelled for motion questions? I'm always unable to answer those types of questions when they're given.

Here are some examples:






Any help is appreciated!

 

[yanujw]

Remember that if velocity is the derivative of displacement, then displacement is the result of integrating velocity. If a particle moves from a to b, then its total distance travelled is , assuming that the particle does not change direction. What the integral actually provides is displacement, but if the particle changes direction then distances need to be calculated for each separate period when the velocity is positive or negative.

 

[AsuTeksu]

Remember that if velocity is the derivative of displacement, then displacement is the result of integrating velocity. If a particle moves from a to b, then its total distance travelled is , assuming that the particle does not change direction. What the integral actually provides is displacement, but if the particle changes direction then distances need to be calculated for each separate period when the velocity is positive or negative.

If only the displacement equation is provided initially rather than the velocity equation, in that case, would you find the velocity equation then integrate it to get the total distance?

 

[Luukas.2]

For total distance travelled, find the position of the particle:

1. at the start of the motion
2. at the end of the motion
3. everywhere it stops (v = 0) during the time interval you are investigating.

Then, draw these positions on a number line.

So, if:

• x = 1 at t = 0
• x = 5 at t = 5
• v = 0 at t = 2, where x = -1

The particle moved from x = 1 to x = -1 (2 units left) then from x = -1 to x = 5 (6 units right) and so travelled 2 + 6 = 8 units

 

[Luukas.2]

If only the displacement equation is provided initially rather than the velocity equation, in that case, would you find the velocity equation then integrate it to get the total distance?

No. You would use the displacement equations for the positions at each time. You would need to find the velocity equation from though, to solve to find out when the particle is stationary (which is the only place that direction can change).

 

[AsuTeksu]

@Luukas.2 Thank you so much for your help again!!!