A car of 120kg mass traveling at 5m/s comes to the rest over a distance of 30m.Find the average retardation (braking acceleration or deceleration) and braking forces?

First, we need to calculate the initial kinetic energy of the car:

Initial kinetic energy = 0.5 * mass * velocity^2
Initial kinetic energy = 0.5 * 120kg * (5m/s)^2
Initial kinetic energy = 0.5 * 120kg * 25m^2/s^2
Initial kinetic energy = 1500 J

Next, we need to calculate the work done by the braking force to bring the car to rest:

Work done = force * distance
1500 J = force * 30m
force = 1500 J / 30m
force = 50 N

Now, we can calculate the average retardation:

Average retardation = (final velocity - initial velocity) / time
Since the car comes to rest, the final velocity is 0 m/s
Average retardation = (0 - 5m/s) / time
Average retardation = -5m/s / time

We also know that the distance traveled is equal to the average velocity multiplied by time:

Distance = average velocity * time
30m = (5m/s + 0) / 2 * time
30m = 2.5m/s * time
time = 30m / 2.5m/s
time = 12s

Now we can calculate the average retardation:

Average retardation = -5m/s / 12s
Average retardation = -0.4167 m/s^2

Therefore, the average retardation (braking acceleration or deceleration) is 0.4167 m/s^2 and the braking force is 50 N.

1. Average Retardation:

Initial velocity, u = 5 m/s
Final velocity, v = 0 m/s
Distance, s = 30 m

Using the equation of motion:
v^2 = u^2 + 2as

0^2 = 5^2 + 2a - 30
a = -0.42 m/s^2

Therefore, the average retardation is 0.42 m/s^2.

2. Braking Forces:

The braking force (F) is given by:
F = ma

where m is the mass of the car (120 kg) and a is the average retardation (0.42 m/s^2).

Therefore, the braking forces are:
F = 120 kg - 0.42 m/s^2
F = 50.4 N