Time when car stopped given initial velocity and acceleration

In summary, the homework statement says that a car has a velocity of 16 m/s at time t = 0. It slows down with an acceleration of -0.50t in m/s^2 for t in seconds, and then stops at t = 6.
  • #1
1MileCrash
1,342
41

Homework Statement



At time t = 0, a car has a velocity of 16 m/s. It slows down w/an acceleration given by -0.50t in m/s^2 for t in seconds. It stops at t =?

Homework Equations





The Attempt at a Solution



v = 16 - 0.5t
16/.5 = t
16 x 2 = t
32 = t

Did I set this up wrong? My answer is incorrect. It even works intuitively, if speed is reduced by .5 every second, starting at 16, it will take 32 subtractions of .5 to equal 0.
 
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  • #2
nothing wrong here. is there a part 2 of the question that you didn't answer?
 
  • #3
No, and even if there was, the system allows partial submissions.
 
  • #4
they goofed up. it happens.
 
  • #5
Okay. Just to make sure they aren't 2 for 2..
"A car moving with an initial velocity of 25 m/s north has a constant acceleration of 3 m/s2 south. After 6 seconds its velocity will be:"

I say 11 m/s south, but this is no option.

x = 25t - 3t^2
v = 25 - 6t
v(6) = 25 - 36
v = -11 (or 11 south, as the option format it.)
 
  • #6
It slows down w/an acceleration given by -0.50t in m/s^2 for t in seconds.

Could this mean the acceleration is not constant? -0.50t m/s2 is different from -0.50 m/s2.
 
  • #7
maybe they do have changing acceleration (didn't notice the "t", sorry)

for problem 2 they want _velocity_ , not distance ...
 
  • #8
lewando said:
Could this mean the acceleration is not constant? -0.50t m/s2 is different from -0.50 m/s2.

I'll try

for problem 2 they want _velocity_ , not distance ...

How is what I found distance?
 
  • #9
I don't know . . . you're ignoring units! where did the 6 t come from ? a = 3 m/s^2
 
  • #10
Guy, y'all were right. Acceleration was not constant. I defined acceleration with a = -.5t + 16 and integrated for velocity function, for a result of 8 seconds when velocity is zero which is correct.

I don't know . . . you're ignoring units! where did the 6 t come from ? a = 3 m/s^2

I differentiated, but I see the error. My position function should have 1.5 as the second coefficient, and the derivative should be back at 3.

So, they didn't goof up at all.
 
Last edited:

Related to Time when car stopped given initial velocity and acceleration

1. What is the formula for calculating the time when a car stops given its initial velocity and acceleration?

The formula for calculating the time when a car stops is t = (v0 - vf) / a, where t is time, v0 is the initial velocity, vf is the final velocity, and a is the acceleration.

2. How do you determine the initial velocity of a car?

The initial velocity of a car can be determined by measuring its speed at the beginning of its motion. This can be done using a speedometer or by measuring the distance the car travels in a certain amount of time.

3. How does acceleration affect the time it takes for a car to stop?

The greater the acceleration, the shorter the time it will take for a car to stop. This is because acceleration is directly proportional to the change in velocity over time, so a higher acceleration will result in a faster change in velocity and thus a shorter stopping time.

4. Can you calculate the time when a car stops if you know its distance traveled and final velocity?

Yes, you can calculate the time when a car stops using the formula t = (vf^2 - v0^2) / (2a), where t is time, vf is the final velocity, v0 is the initial velocity, and a is the acceleration. This formula assumes constant acceleration and can be derived from the original formula by substituting vf = v0 + at.

5. How does the weight of a car affect its stopping time?

The weight of a car does not directly affect its stopping time. However, a heavier car will require a greater force to stop, which may result in a longer stopping distance. Additionally, a heavier car may have different acceleration capabilities, which can affect the time it takes for the car to stop.

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