velocity? displacement? acceleration?

Question

A driver of a car traveling at 15.0 m/s applies the brakes, causing a uniform acceleration of -2.0 m/s^2. How long does it take the car to accelerate to a final speed of 10.0 m/s? How far has the car moved during the braking period?

the textbook has the equation to get the Time but i need the Displacement (how far)...but to get the Displacement i need the Time. anyone help me please??

Answer 1

given Vi=15m/s Vf=10m/s a=2.0m/s^2

Find=delta T n delta X

Solution
10 minus 15 divided by 2 gives u delta T
then
delta X=Vi minus vf divided by 2 times delta T

Answer 2

Well, you know that the car will take 2.5 seconds to reach that speed because every second it slows 2 m/s. Since the car has to slow from 15m/s to 10 m/s, it has to slow 5 m/s. At an acceleration of -2.0m/s^2 we can determine that it will take
2m/s^2 x 2.5 to slow 5 m/s.

Now that you have the time it takes for the car to slow, you can figure out the rest.

Answer 3

d-displacement
vi-initial velocity
vf-final velocity
a-accleration
t-time

to find the time:
d-N/A
vi-15m/s
vf-10m/s
a- -2m/s
t- ?

vf=vi+at
10=15+-2t
-5=-2t
2.5=t

then... to find displacement:
d=?
vi=15m/s
vf=10m/s
a= -2m/s/s
t=2.5s

d=vit+1/2at^2
d=15(-2)+1/2(-2)2.5^2
d=-30+-1(6.25)
d=-30+-6.25
d=36.25m

I hope this helps!

Answer 4

Use these equations:

a = (v_final - v_initial) / t

(they give you "a", "v_final" and "v_initial", so solve for "t").

Then:

d = (v_intial)t + at²/2