How to solve SUVAT problem without using relative velocity

In summary: If you use the SUVAT equations, you would use different values for the initial velocity (u) and acceleration (a) for each particle, but the final velocity (v) and displacement (x) should be the same in both equations. So you can solve for either of those variables in one equation and then use the same value in the other equation. In summary, when calculating the time taken for particle A to catch up with particle B, you can either work out the relative velocity or use the SUVAT equations of motion to equate the positions and solve for the time. Both methods will lead to the same solution, but using separate equations may be more straightforward for more complicated particle motions with separate accelerations.
  • #1
rollcast
408
0

Homework Statement


Calculate the time taken for particle A to catch up with particle B.
See attachment for variables.

I worked out the answer by finding the relative velocity of A wrt B but apparently there's another method I should have/could have used to solve it?


Homework Equations



SUVAT equations of motion


The Attempt at a Solution



See attachment.

Thanks
AL
 

Attachments

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  • #2
You could write separate expressions for the positions of each particle, then equate them to find when the positions are the same.
 
  • #3
So call the final displacement when they meet, x, get 2 equations and then solve them as simultaneous equations?

Is there any advantage to that approach compared to just working out the relative velocity?
 
  • #4
rollcast said:
So call the final displacement when they meet, x, get 2 equations and then solve them as simultaneous equations?

Is there any advantage to that approach compared to just working out the relative velocity?

Either approach could be transformed into the other via suitable algebraic slight of hand. The separate equation approach has the advantage that it may be more straightforward when the particle motions are more complicated. For example, suppose that both particles also had separate accelerations?
 
  • #5
gneill said:
Either approach could be transformed into the other via suitable algebraic slight of hand. The separate equation approach has the advantage that it may be more straightforward when the particle motions are more complicated. For example, suppose that both particles also had separate accelerations?

But the relative approach will still work with accelerations?

Do you just work out the acceleration of one relative to the other or do you have to use v=u+at for both and then then subtract the 2?
 
  • #6
rollcast said:
But the relative approach will still work with accelerations?

Do you just work out the acceleration of one relative to the other or do you have to use v=u+at for both and then then subtract the 2?

It amounts to the same thing.
 

Related to How to solve SUVAT problem without using relative velocity

1. What is SUVAT and why is it important in solving problems?

SUVAT is a set of equations used in kinematics to solve problems related to motion. It stands for displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). These equations are important because they allow us to calculate unknown variables and understand the motion of objects.

2. Can SUVAT problems be solved without using relative velocity?

Yes, SUVAT problems can be solved without using relative velocity. The equations only require the values of displacement, initial velocity, final velocity, acceleration, and time to solve for unknown variables. Relative velocity is not necessary for these calculations.

3. What are the steps to solve an SUVAT problem without using relative velocity?

The steps to solve an SUVAT problem without using relative velocity are:1. Identify the given variables and the unknown variable.2. Use the appropriate SUVAT equation to solve for the unknown variable.3. Substitute the given values into the equation.4. Solve for the unknown variable using algebraic manipulation.

4. Are there any tips for solving SUVAT problems without using relative velocity?

Yes, here are some tips for solving SUVAT problems without using relative velocity:- Make sure to use the correct equation for the given problem.- Keep track of units and make sure they are consistent throughout the calculation.- Draw a diagram to visualize the problem and help you understand the given values and unknown.- Break down the problem into smaller steps to make it more manageable.

5. Can SUVAT equations be used for any type of motion?

Yes, SUVAT equations can be used for any type of motion as long as the motion is constant. This means that the acceleration remains constant throughout the motion. If the acceleration is not constant, other equations such as the equations of motion with calculus may need to be used.

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