Problem:
A car moving at 40 km/hr is to be stopped by applying brakes in the next 4 meters. If the car weighs 2000 kg, what average force must be applied on it?

Solution:

To find the average force required to stop the car, we need to use the formula:

Force (F) = mass (m) × acceleration (a)

We can calculate the acceleration using the equation of motion:

v^2 = u^2 + 2as

Where v is the final velocity (0 m/s), u is the initial velocity (40 km/hr), a is the acceleration, and s is the distance (4 meters).

Step 1: Convert the initial velocity from km/hr to m/s.

Given: initial velocity (u) = 40 km/hr

To convert km/hr to m/s, we use the conversion factor: 1 km/hr = 0.278 m/s

So, the initial velocity in m/s is:

40 km/hr × 0.278 m/s = 11.12 m/s

Step 2: Calculate the acceleration (a) using the equation of motion.

We know that the final velocity (v) is 0 m/s, the initial velocity (u) is 11.12 m/s, and the distance (s) is 4 meters.

Using the equation v^2 = u^2 + 2as, we can rearrange it to solve for acceleration (a):

a = (v^2 - u^2) / (2s)

Substituting the given values:

a = (0^2 - 11.12^2) / (2 × 4) = -123.54 m/s^2

Note: The negative sign indicates that the acceleration is in the opposite direction of the initial velocity.

Step 3: Calculate the force (F) required to stop the car using the formula F = m × a.

Given: mass (m) = 2000 kg, acceleration (a) = -123.54 m/s^2

F = 2000 kg × -123.54 m/s^2 = -247,080 N

Step 4: Find the average force.

Since we are interested in the magnitude of the force, we can ignore the negative sign.

Average force = 247,080 N

Thus, the average force that must be applied to stop the car is 247,080 N.