Consider someone driving down the highway at 70 miles per hour (31.3 m/s). The total mass of the driver and their car (as well as everything else in the car) is 1600kg.

Part A- How much work must friction do to make the car stop?

Part B- A tree suddenly falls on the highway 55m in front of the car, and the driver just barely manages to stop before hitting the tree. What is the magnitude of the force of friction necessary to do the work you calculated in part A just before the car hits the tree?

Part C- Now imagine that the driver had been traveling at 75 miles per hour (33.5 m/s) at the start instead. The coefficient of friction is still the same, so the force from friction will still be what you calculated in part B, which means the work done by friction will be the same as in part A. Under these circumstances, what will the car's speed be when it hits the tree?

A. -783752 J

B. -14250 N

C. 11.94 m/s

Explanation:

A. Work done is given as the change in kinetic energy, hence,

W = ΔKE

W = KE(final) - KE(initial)

KE(final) = 0 since the car comes to rest.

=> W = -KE(initial)

W = -½*m*u²

W = -½ * 1600 * 31.3²

W = -783752J

The negative indicates that the force responsible for the work is acting opposite the direction of the motion.

B. Work done is also given as:

W = F * d

Where F = Force

d = distance moved

=> F = W/d

F = -783752/55

F = -14250 N

The negative indicates that the force acts against the direction of motion.

C. The initial velocity, u, is now 33.5m/s.

Going back to the formula for work done in A,

W = KE(final) - KE(initial)

KE(final) is not zero in this case because the car doesn't come to rest before collision, hence,

W = ½*m*v² - ½*m*u²

Since the force is the same, then, work done is the same,

-783752 = ½*m*v² - ½*1600*33.5²

-783752 = ½*m*v² - 897800

½*m*v² = 897800 - 783752

½*m*v² = 114048

v² = (114048 * 2) / (1600)

v² = 142.56

v = 11.94 m/s

answer; how far out of place which the object finished relative to the starting location;

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.