How long will it take for Sam to catch up to John?

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In summary, Homework Statement:Sam is running at 3.8 m/s and is 75 m behind John who is running at a constant velocity of 4.2m/s. If Sam accelerates at 0.15m/s^2, how long will it take him to catch John?
  • #1
harujina
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Homework Statement



Sam is running at 3.8 m/s and is 75m behind John who is running at a constant velocity of 4.2m/s. If Sam accelerates at 0.15m/s^2, how long will it take him to catch John?

Homework Equations



d = (vf+vi/2)t
vf = vi + at
d = vit + 1/2at^2
vf^2 = vi^2 + 2ad
d = vft - 1/2at^2

The Attempt at a Solution



I have asked this before, but have now come back with a little more understanding than before.
I've done the following so far:

Xs (displacement of Sam) = viΔt + 1/2aΔt^2
= (3.8m/s)Δt + (0.075m/s^2)Δt^2

Xj (displacement of John) = 75 + 4.2m/sΔt

[-> from: (xf-xi) = VavΔt
xf = xi + VavΔt ]

---

... Ok so now I do (3.8m/s)Δt + (0.075m/s^2)Δt^2 = 75 + 4.2m/sΔt
to find the time when they are in the same position/displacement, correct?

But I'm so confused as to what I would do after that?

EDIT; Also, I got 1005.33s for the time, and I don't think that's right?
 
Last edited:
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  • #2
What you got is a quadratic equation where delta t is unknown. Solve it.
 
  • #3
ax^2 + bx + c = 0?

This may be a stupid question but how would I know which variable goes for which coefficient?
(I need to brush up on my math...)
 
  • #4
harujina said:
ax^2 + bx + c = 0?

This may be a stupid question but how would I know which variable goes for which coefficient?
(I need to brush up on my math...)

##x## is the unknown. In your case, the unknown is ##\Delta t##. You should be able to match the other symbols.
 
  • #5
Okay I think I get it but then what was this for: (3.8m/s)Δt + (0.075m/s^2)Δt^2 = 75 + 4.2m/sΔt ?
I thought I was trying to find time with that?
 
  • #6
I do not understand your questions. What does ##\Delta t## mean to you?
 
  • #7
time, is it not?
 
  • #8
It is time, and it is what you are after. What is not clear to you?
 
  • #9
Well, my teacher said I had to find the position/displacement of both Sam and John, which I did:
(3.8m/s)Δt + (0.075m/s^2)Δt^2 for Sam and
75 + 4.2m/sΔt for John

and if I do: (3.8m/s)Δt + (0.075m/s^2)Δt^2 = 75 + 4.2m/sΔt
won't that give me time? So why would I have to do the quadratics equation?
Or am I doing something wrong here...
 
  • #10
harujina said:
and if I do: (3.8m/s)Δt + (0.075m/s^2)Δt^2 = 75 + 4.2m/sΔt
won't that give me time? So why would I have to do the quadratics equation?

Because the equation you got is a quadratic equation. It will give you time - when you solve it.
 
  • #11
OH, now I understand what my teacher was saying!
I got 32s, is that right?
 
  • #12
You can check your answer yourself: you have the formula for displacement for Sam, and the formula for John. Do you get the same displacements at 32 s?
 
  • #13
I got 34.4 seconds
 
  • #14
(3.8m/s)(32s) + (0.075m/s^2)(32s)^2 = 198.4 m
75 + 4.2m/s(32s) = 209.4 m

so I am a bit off...
this is what i did:
---
(3.8m/s)Δt/t + (0.075m/s^2)Δt^2 = 75 + 4.2m/sΔt/t
3.8m/s - 3.8m/s + (0.075m/s^2)Δt^2 = 75 + 4.2m/s - 3.8m/s
(0.075m/s^2)Δt^2 / 0.075m/s^2 = 75 + 4.2m/s - 3.8m/s / 0.075m/s^2
Δt^2 = 75 + 4.2m/s - 3.8m/s / 0.075m/s^2
(square root)Δt = (square root)1005.33 s

Δt = 32 s
 
Last edited:
  • #15
I do not know what you are doing, but you are not solving the equation correctly.

First you need to bring it to the standard form: ## a \Delta t^2 + b \Delta t + c = 0 ##.

Then use the (supposedly) well-known formula for its roots.
 
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  • #16
Okay I finally got it. Thank you so much and sorry for all the troubles!
 
  • #17
No trouble at all. I hope this has been useful for you :)
 

1. What is the definition of kinematics in physics?

Kinematics is the branch of physics that deals with the motion of objects without considering the forces that cause the motion. It focuses on describing the position, velocity, and acceleration of objects over time.

2. What is the basic equation for kinematics?

The basic equation for kinematics is the displacement formula: d = v0t + 1/2at2, where d is the displacement, v0 is the initial velocity, a is the acceleration, and t is the time.

3. How do you solve kinematics problems?

To solve a kinematics problem, you need to follow these steps:

  • Identify the known and unknown variables
  • Select the appropriate equation(s) based on the given information
  • Plug in the known values into the equation(s)
  • Solve for the unknown variable
  • Check your answer for accuracy and units

4. What are the three kinematic equations?

The three kinematic equations are:

  1. d = v0t + 1/2at2 (displacement formula)
  2. v = v0 + at (velocity formula)
  3. v2 = v02 + 2ad (acceleration formula)

5. What are some common units used in kinematics equations?

Some common units used in kinematics equations are:

  • Distance/Displacement: meters (m)
  • Time: seconds (s)
  • Velocity: meters per second (m/s)
  • Acceleration: meters per second squared (m/s2)

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