When will one car overtake the other? (acceleration,veolcity,time)

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In summary, at the moment the car begins to accelerate, the truck with a constant velocity of 21 m/s passes in the next lane. The car will travel 147 m before overtaking the truck.
  • #1
drinkingstraw
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As a traffic light turns green, a waiting car starts with a constant acceleration of 6.0 m/s^2.At the instant the car begins to accelerate, a truck with a constant velcoity of 21 m/s pass in the next lane.

(a) How far will the car travel before it overtakes the truck?
(b) How fast will the car be traveling when it overtakes the truck?

Calculations (a) :

Car:
Vi = 0 m/s
Vf = ?
Acceleration = 6.0 m/s^2

Truck:
Vi = 21 m/s
Vf = 21 m/s
Acceleration = 0 m/s^2


* in order to figure out (a), the deltaD's of both the car and truck must be equal
- I'm not to sure if the deltaT will be the same but it seems as though the intial time is the same

This is all I know so far; I've been trying to sub in equations but nothing seems to work. Could someone please guide me in the right direction. Thanks :)
 
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  • #2
Can you write down equations for the distance covered by the car and the truck as a function of time?
 
  • #3
CompuChip said:
Can you write down equations for the distance covered by the car and the truck as a function of time?

The equations I could use are:
deltaD = [(vi + vf)/2] x deltaT
delta D = vi x deltaT + 0.5 x acceleration x deltaT^2
deltaD = vf x deltaT - 0.5 x acceleration x deltaT^2
deltaD = (vf^2 - vi^2)/(2 x acceleration)
 
  • #4
I suggest first calculating after what time the car overtakes the truck, so find the delta T.

For the truck, you know the average velocity and there is no acceleration. For the car, you know the acceleration and initial velocity. Which two of the four formulas do you think are useful then?
 
  • #5
CompuChip said:
I suggest first calculating after what time the car overtakes the truck, so find the delta T.

For the truck, you know the average velocity and there is no acceleration. For the car, you know the acceleration and initial velocity. Which two of the four formulas do you think are useful then?

For the truck:
deltaD = [(vi + vf)/2] x deltaT

For the car:
delta D = vi x deltaT + 0.5 x acceleration x deltaT^2

Would I use these two?
 
  • #6
What is vi for the car?
What equation to you get for deltaT?
What is its solution?
 
  • #7
CompuChip said:
What is vi for the car?
What equation to you get for deltaT?
What is its solution?

For the truck:
deltaD = [(vi + vf)/2] x deltaT
deltaT = 2deltaD/(vi+vf)

For the car:
delta D = vi x deltaT + 0.5 x acceleration x deltaT^2
how would I rearrange this one?

*** how would I solve for these without knowing the deltaD value?
 
  • #8
drinkingstraw said:
* in order to figure out (a), the deltaD's of both the car and truck must be equal

You will get a quadratic equation, which should be easy to solve because you already know one solution (the one you don't want).
 
  • #9
CompuChip said:
You will get a quadratic equation, which should be easy to solve because you already know one solution (the one you don't want).

You said to first solve for time but in order to do so, the equations ask for a value for deltaD. Are you saying I would get a quadratic equation for time?

For the car:
deltaD = 3deltat^2

For the truck:
deltaD = 21deltat

Is this what I was supposed to do?

Next I changed the equations to deltaT = and then I put one equal to the other.

deltaD/3 = deltaD^2/21
= 441/3 = deltaD
= 147 m

Is this correct?
 
Last edited:

1. How do you calculate the time it takes for one car to overtake another?

The time it takes for one car to overtake another can be calculated using the formula: t = (v2 - v1) / (a1 - a2), where t is the time, v1 and v2 are the initial velocities of the two cars, and a1 and a2 are the accelerations of the two cars.

2. How does the acceleration of the cars affect the time it takes for one to overtake the other?

The acceleration of the cars directly affects the time it takes for one to overtake the other. The larger the difference in acceleration between the two cars, the shorter the time it will take for the faster car to catch up and overtake the slower car.

3. Is it possible for a slower car to overtake a faster car?

Yes, it is possible for a slower car to overtake a faster car. This can happen if the slower car has a higher acceleration rate than the faster car. In this case, the slower car may initially be behind the faster car, but it will catch up and overtake it due to its higher acceleration.

4. Can the distance between the two cars affect the time it takes for one to overtake the other?

Yes, the initial distance between the two cars can affect the time it takes for one to overtake the other. The shorter the distance between the two cars, the shorter the time it will take for them to meet. This is because the faster car will have a shorter distance to cover to catch up to the slower car.

5. How does the velocity of the cars change during the overtaking process?

The velocity of both cars will change during the overtaking process. The faster car will initially have a higher velocity and will gradually decrease as it catches up to the slower car. On the other hand, the slower car will initially have a lower velocity and will gradually increase as it is overtaken by the faster car.

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