Seemingly simple kinematics question

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In summary, the question is asking for the maximum velocity a car will reach over a distance of 105m, starting and stopping at rest, given accelerations of +7.5m/s^2 and -10m/s^2. Various approaches were suggested, including using the formula v^2 = vi^2 + 2(s-si), breaking the motion into two segments, and using calculus to find the maximum velocity. Ultimately, it was found that the maximum velocity can be calculated by using the formula v^2 = vi^2 + 2(s-si), with the final velocity at the end of acceleration being the same as the initial velocity at the start of deceleration.
  • #1
macmav
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This question appears to be very simple at first but has stumped me for hours now:

we are given 2 accelerations
+7.5m/s^2 and -10m/s^
a car brakes and accelerates at these rates
over 105m, what is the maximum velocity the car will reach, starting and stopping at rest?


Originally I was thinking to use one of the three constant acceleration equations but I always end up going nowhere (0=0, 7.5t=10t) etc. The closest I've gotten was plotting a velocity-time graph but I can think of no way to find the constant to be added onto the line -10t to make the area under it and 7.5t equal 105m. I believe I just have to use the formula v^2 = vi^2 + 2(s-si) but every time I try I'm stuck!

If some1 can point me in the right direction itd be of awesomeness! Thank you for your time.
 
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  • #2
macmav said:
I believe I just have to use the formula v^2 = vi^2 + 2(s-si) but every time I try I'm stuck!
That's the equation I would use. Break the motion into two segments: Speeding up (a1 = 7.5 m/s^2) and slowing down (a2 = -10 m/s^2). Don't forget that the distance traveled in each segment must add up to the total distance given.
 
  • #3
You're right about using the formula [tex]v^2 - u^2 = 2as[/tex]. Write down two equations, one for the part where the car accelarates, and an other when the car decelarates. Add the two equations. (Make sure you get the signs right)
 
  • #4
The maximum speed will be the speed at the end of the acceleration, just before the driver applies the brakes. Once the brakes is applied the speed of the car will start to decrease - that is the whole idea behind braking!
 
  • #5
hi , i thought this problem is to be solved by maxima/minima of calculus but following above suggestions i arrived at the following,

1) The final velocity when the car is accelerating is the initial velocity when it is decelerating (brakes applied).
2) So i used the formula suggested above and found the vmax to be 30 m/sec and the distance/displacement achieved is 60 meters from starting pt and t=4 sec (applying the brake at t=4 sec).
3) i just tried to see what happens when the driver applied the brakes at t=5 secs, i got vmax of 37.5 but using this as initial velocity on the second part i found that final velocity is not zero, (34.37 m/sec).

I don't know the principle behind on why such simple equation for like this will yield the max velocity. Thanks to all.
 

1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion.

2. What is a seemingly simple kinematics question?

A seemingly simple kinematics question is one that involves analyzing the motion of an object based on its initial position, velocity, and acceleration, without considering any external forces.

3. What are the basic equations used in kinematics?

The basic equations used in kinematics are the equations of motion: - x = x0 + v0t + ½at2- v = v0 + at- v2 = v02 + 2a(x−x0)- x = x0 + ½(v0 + v)twhere x is the final position, x0 is the initial position, v is the final velocity, v0 is the initial velocity, a is the acceleration, and t is the time.

4. Is kinematics only applicable to objects moving in a straight line?

No, kinematics can also be applied to objects moving in a curved path or in two or three dimensions. In these cases, the equations of motion may be more complex, but the principles of kinematics still apply.

5. How is kinematics used in real-world applications?

Kinematics is used in many real-world applications, such as designing and analyzing the motion of machines and vehicles, predicting the trajectory of projectiles, studying the movement of planets and celestial bodies, and understanding the mechanics of sports and athletic movements.

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