As the driver steps on the gas pedal, a car of mass 1 140 kg accelerates from rest. during the first few seconds of motion, the car's acceleration increases with time according to the expression below, where t is in seconds and a is in m/s2. a = 1.14 t - 0.210 t2 + 0.240 t3 (a) what is the change in kinetic energy of the car during the interval from t = 0 to t = 2.60 s? j (b) what is the minimum average power output of the engine over this time interval? w (c) why is the value in part (b) described as the minimum value?

(a)

(b) P = 6309.6981 W

(c) Value in above part is described as minimum because there would have been power loss in the actual system to achieve this acceleration from the state of rest.

Explanation:

Given:

mass of car, m = 1140 kg

expression of acceleration,

where "t" is time in seconds

initial time,

final time,

(a)

We know,

Kinetic Energy

∴

(b)

We know,

Power

P = 6309.6981 W

(c)

Value in above part is described as minimum because there would have been power loss in the actual system to achieve this acceleration from the state of rest.

a 2,000 calorie based diet.

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.