Mass of car 1000k that is brought to rest from the speed of 50m/s in a distance of 100m.Find the breaking force of the car assuming that is constant and there is constant resistance to motion of 100N?

To find the braking force of the car, we can use the work-energy principle. The work done by the braking force is equal to the initial kinetic energy of the car minus the work done by the resistance force.

The initial kinetic energy of the car is given by:

KE_initial = 0.5 * m * v^2
KE_initial = 0.5 * 1000 * 50^2
KE_initial = 1,250,000 J

The work done by the resistance force is equal to the force multiplied by the distance:

Work_resistance = F_resistance * d
Work_resistance = 100 * 100
Work_resistance = 10,000 J

Therefore, the work done by the braking force is:

Work_braking = KE_initial - Work_resistance
Work_braking = 1,250,000 - 10,000
Work_braking = 1,240,000 J

Since work done by the braking force is equal to the braking force multiplied by the distance, we can find the braking force:

Work_braking = F_braking * d
1,240,000 = F_braking * 100
F_braking = 12,400 N

Therefore, the braking force of the car is 12,400 N.

Given:

- Mass of car (m) = 1000 kg
- Initial velocity (u) = 50 m/s
- Final velocity (v) = 0 m/s
- Distance traveled (s) = 100 m
- Resistance force (F_r) = 100 N

Formula for work done by braking force (W_b):

```
W_b = F_b - s
```

Formula for change in kinetic energy (ΔKE):

```
ΔKE = 1/2 - m - (v^2 - u^2)
```

According to the work-energy theorem:

```
W_b + W_r = ΔKE
```

Substituting the values:

```
F_b - s + F_r - s = 1/2 - m - (v^2 - u^2)
```

```
F_b - 100 + 100 - 100 = 1/2 - 1000 - (0^2 - 50^2)
```

```
100 - F_b + 10000 = -125000
```

```
F_b = -2250 N
```

Ignoring the negative sign, the braking force of the car is 2250 N.