Question

a car whose brakes can produce an acceleration of 6 m/s^2 is traveling at 30m/s when its brakes are applied...what is the cars speed 2s later and what is the total time needed for the car to stop

Answer 1

\[V_i=30m/s\]\[a=-6m/s^2\]The car's speed (Vf) at any time while braking can be figured out using the kinematic equation:\[V_f=V_i+at\]To figure out how long it takes the car to stop simply set Vf to 0m/s and solve the above equation for time.

Answer 2

is the answer 64

Answer 3

\[\large 30m/s+(-6m/s^2)(2)=?m/s\]

Answer 4

If you're confused let's discuss it a moment

Answer 5

Since acceleration is constant you can use the kinematic equation:\[V_f=V_i+at\]That formula is simply saying that the final velocity will equal the initial velocity + (the acceleration multiplied by the time).

In the problem you're given this info:
1) 30 meters per second = initial velocity (Vi)
2) -6m/s^2 = acceleration (a)...it's negative because the acceleration is due to the braking of the car (opposite direction to the car's motion)
3) 2 seconds = time.

When you plug all that info into the equation you get:
\[\large V_f= 30m/s+(-6m/s^2)(2)=18m/s \]

Answer 6

okay what was confusing me was the S squared,

Answer 7

so now we would have 30m/s-18m/s? is that correct?

Answer 8

The S^2 just means meters per second, per second. When you write it out maybe it would help if you did this:

\[\large V_f= \frac{30m}{s}+(-6\frac{m}{s^2})(2s)=18m/s\]As you can see above, one of the S's in the denominator of the fraction on the right cancels out with the 2s.

Answer 9

ohhh okay

Answer 10

Ok...so where are we at.. The speed after 2 seconds will be 18 m/s.

For the second part of the question it's asking how long it will take the car to stop while braking. The same formula can be used but this time you already know the final speed will be 0 m/s and now you need to just solve it for t:\[\large V_f=V_i+at\]\[\large 0m/s=30m/s+(-6m/s^2)t\]Solving for t you get:\[t=\frac{V_f-Vi}{a}\]Now plug in the values:\[t=\frac{0m/s-30m/s}{-6m/s^2}=5seconds\]

Answer 11

that makes more sense once it's actually broken down the way you did it.
Thank you

Answer 12

no problem :)