last point from backward difference formula

Question

What will be an ideal response?

Answer 1

```
first.observed[numPoints-1]
= observed[numPoints-1] - observed[numPoints-2];
}

void ObservedFunction::findSecond(ObservedFunction& second)
{
// ensure array second is of correct size (2 smaller)
if (second.numPoints != numPoints - 2) {
second.numPoints = numPoints - 2;
second.deleteFunction();
second.observed = new double [second.numPoints];
}

for (int i=1; i < numPoints - 1; i++)
second.observed[i-1] = observed[i+1] - 2 * observed[i] +
observed[i-1];
}

double ObservedFunction::getValue(int index) const
{
return observed[index];
}

istream& operator>> (istream& is, ObservedFunction& of)
{
for (int i = 0; i < of.numPoints; i++) {
cin >> of.observed[i];
}
return is;
}

ostream& operator<< (ostream& os, const ObservedFunction& of)
{
cout << setiosflags(ios::fixed) << setprecision(1);
for (int i = 0; i < of.numPoints; i++)
cout << setw(10) << of.observed[i];
cout << endl;
return os;
}
class RaceCar
{
public:
RaceCar(){}
RaceCar(int, double);
void deleteRaceCar(); // free mem
void findForce();

private:
ObservedFunction distance;
ObservedFunction velocity;
ObservedFunction deaccel;
double* force;
int numPoints;
double mass;

friend istream& operator>> (istream&, RaceCar&);
friend ostream& operator<< (ostream&, const RaceCar&);
};

RaceCar::RaceCar(int points, double carMass)
:distance(points), velocity(points), deaccel(points-2)
{
numPoints = points;
mass = carMass;
force = new double [points-2];

for (int i = 0; i < points-2; i++)
{
force[i]=0;
}
}

void RaceCar::deleteRaceCar()
{
delete[] force;
distance.deleteFunction();
velocity.deleteFunction();
deaccel.deleteFunction();
}

void RaceCar::findForce()
{
distance.findFirst(velocity);
distance.findSecond(deaccel);
for (int i = 0; i < numPoints-2; i++)
force[i] = mass * deaccel.getValue(i);

}

istream& operator>> (istream& is, RaceCar& rc)
{
cin >> rc.distance;
return is;
}

ostream& operator<< (ostream& os, const RaceCar& rc)
{
int i;

cout << setw(-12) << "Distance:" << rc.distance << endl
<< setw(-12) << "Velocity:" << rc.velocity << endl
<< setw(-12) << "Deaccel:" << setw(11) << " "
<< rc.deaccel << endl << setw(-12) << "Force:" << setw(13)
<< " ";
for (i = 0; i < rc.numPoints-2; i++) {
cout << setw(10) << rc.force[i];
}
cout << endl;
return os;
}

int main()
{
int num;
double mass;
RaceCar car;

cout << endl << "What is the mass of the car? => ";
cin >> mass;
cout << endl << "How many points were observed? => ";
cin >> num;
car = RaceCar(num, mass);
cout << endl << "Please enter the " << num << " distances => ";
cin >> car;
car.findForce();

cout << endl << car << endl;

return 0;
}

```