Vehicle of mass 1000kg that is brought to rest from a speed of 50m/s in a distance of 100m.Find the breaking force of vehicle assuming that is constant and that there is constant resistance of 100N?

To find the braking force of the vehicle, we can use the equation for work done by a force:

Work = Force x Distance

The work done by the braking force is equal to the initial kinetic energy of the vehicle:

Work = 0.5 * mass * velocity^2

Given:
mass = 1000 kg
velocity = 50 m/s

Work = 0.5 * 1000 * 50^2
Work = 0.5 * 1000 * 2500
Work = 1250000 J

The work done by the braking force is also equal to the sum of the work done by the braking force and the work done by the resistance force:

Work = Force x Distance + Resistance force x Distance

1250000 = Force x 100 + 100 x 100
1250000 = Force x 100 + 10000

Solving for Force:

Force x 100 = 1250000 - 10000
Force x 100 = 1240000
Force = 1240000 / 100
Force = 12400 N

Therefore, the braking force of the vehicle is 12400 N.

Given:

- Mass of the vehicle, m = 1000 kg
- Initial speed, u = 50 m/s
- Final speed, v = 0 m/s
- Distance traveled, s = 100 m
- Constant resistance force, F_r = 100 N

Equation of Motion:

$$v^2 = u^2 + 2as$$

where a is the acceleration of the vehicle.

Solving for Acceleration:

$$0^2 = 50^2 + 2a(100)$$

$$a = -12.5 \ m/s^2$$

(Negative sign indicates the acceleration is in the opposite direction of motion)

Breaking Force:

The breaking force is the force that is applied to the vehicle to bring it to rest. It is equal to the sum of the frictional force and the force due to acceleration:

$$F_b = F_r + ma$$

$$F_b = 100 N + (1000 kg)(-12.5 m/s^2)$$

$$F_b = -11500 N$$

Therefore, the breaking force of the vehicle is 11500 N.