Homework Help: Kinematics car acceleration question

1. Aug 31, 2015

Janiceleong26

1. The problem statement, all variables and given/known data

For part c ii) of this question, the new distance is now 1/4 of the previous distance as both acceleration are the same.

But why are both the acceleration the same?

2. Relevant equations
v^2= u^2 +2as

3. The attempt at a solution
I know that the method is by using the above equation, and taking v as 0, we get s = u^2/2a.
So when the initial speed is now halved, we get s' = (u/2)^2 /2a , and ∴ s' = u^2/8a , which is ¼ of the previous distance.

But why are the acceleration the same for both cases?

2. Sep 1, 2015

swerider

The deceleration (negative acceleration because it is slowing down) is the same in both cases because it is assumed that the same braking effort was used in both cases. Remember accel/decel is the rate of change of velocity, and in both cases the car is slowing down at the same rate, regardless of initial velocity.

3. Sep 1, 2015

Janiceleong26

But how do we know that same braking effort is used in both cases? Is it because the resistive force are the same for both cases too?

4. Sep 1, 2015

haruspex

I agree with you - there is no sound basis for assuming the deceleration is the same. The driver, presumably, merely requires to stop before reaching the obstacle, but has no reason to stop well short of it. If the initial speed is lower, the driver may choose to decelerate more gently, and/or start braking later. It's a poorly specified question.
If I had to guess, I'd go for covering the same distance and starting to brake at the same point in time, but decelerating more gently.

5. Sep 1, 2015

Janiceleong26

Yeah. Are the resistive force acting on the car at stage 2 the same for both cases? Since same car, same driver..? But if the car is moving at a slower speed, then shouldn't the counter forces (e.g. Air resistance) be lesser?
Because in determining the resistive force, we can know the deceleration of the car (whether they are the same )

6. Sep 1, 2015

haruspex

The graph shows a constant deceleration, so I doubt air resistance is to be considered. The difficulty is knowing how the driver will behave. With a lower speed, i think the driver would not brake as hard. Why would the driver want to stop a long way in front of the obstruction?

7. Sep 1, 2015

Janiceleong26

Haha..true. This question isn't clear enough. Thanks anyways !