How far will a car travel when decelerating from 60km/h to 10km/h in 2.0s?

[xcompulsion]

A car traveling at 40km/h has it's speed reduced to 10km/h in 2.0s. Assuming that the same deceleration would be in effect, find how far the car will travel in coming to rest from a speed of 60km/h?

 

[hage567]

What are you thoughts on how to start this problem?

 

[xcompulsion]

What are you thoughts on how to start this problem?

I'm thinking about calculating the acceleration using the givens from the first part, to calculate the second part.

so using the equation,
v2^2 = v1^2 + 2(a)(t)

But what has gotten me really puzzled is the seconds, the hours, and the kilometers.

 

[hage567]

That's the right approach, but that equation is not quite right. That t should be a d (as in distance). Check for another equation.

You will need to convert your quantities so they are all in the same units. I usually work in meters and seconds in these questions. I would start with that before you do anything else.

 

[xcompulsion]

That's the right approach, but that equation is not quite right. That t should be a d (as in distance). Check for another equation.

You will need to convert your quantities so they are all in the same units. I usually work in meters and seconds in these questions. I would start with that before you do anything else.

Okay, so after converting all the units to m/s..

first part:
v1 = 40km/h = 11.11m/s
v2 = 10km/h = 2.8m/s
t=2.0s
a = v/t = (2.8m/s - 11.11m/s) / 2.0s = -4.155m/s^2

second part:
v1 = 60km/h = 16.67m/s
v2 = 0km/h = 0m/s
a = -4.155m/s^2
d = ?

v2^2 = v1^2 + 2(a)(d)
0 = (16.67)^2 + 2(-4.155)(d)
0 = 277.9 + (-831)(d)
d = 831 - 277.9
d = 553.1m/s

However, the correct answer to this question is 0.033km..

 

[hage567]

That -831 is wrong, you missed the decimal place!

Also, you didn't solve for d correctly. There should be division involved. Try again.

 

[xcompulsion]

v2^2 = v1^2 + 2(a)(d)
0 = (16.67)^2 + 2(-4.155)(d)
0 = 277.9 + (-8.31)(d)
-277.9 / -8.31 = (-8.31)(d) / (-8.31)
d = 33.44m

so, 33.44/1000 = 0.033km!

thank you so much

 

[hage567]

You're welcome!