Acar is traveling at 24.0 m/s when the driver suddenly applies the brakes, causing the car to slow down with constant acceleration. the car comes to a stop in a distance of 120 m. how fast was the car moving when it was 60.0 m past the point where the brakes were applied?

The answer to your question is : vf = 15.18 m/s

Explanation:

Data

vo = 24 m/s

d = 120 m

vf = ? when d = 60.0 m

Formula

              vf² = vo²  + 2ad

For d =100m

            a = (vf² - vo²) / 2d

            a = (0 -24²) / 2(100)

            a = -576/200

             a = 2.88 m/s²

Now, when d = 60

        vf² = (24)² - 2(2.88)(60)

        vf² = 576 - 345.6

        vf² = 230.4

        vf = 15.18 m/s

17 m/s

Explanation:

Data

initial speed, Vi = 24 m/s

distance travelled, x = 120 m

final speed, Vf = 0 m/s

With help of the next Uniformly Accelerated Motion equation, we can compute car acceleration.

Vf² = Vi² + 2ax

a = Vf² - Vi²/(2x) 

a = 0² - 24²/(2*120) 

a = -2.4 m/s²

Now, the final speed is the unknown and the distance is 60 m:

Vf² = Vi² + 2ax

Vf = √(24² + 2*(-2.4)*60)

Vf = 17 m/s

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2