A car of mass 1 tone is brought to rest from a speed of 40 m/s in a distance of 80 m. Find the braking force of the car assuming that it is constant and that there is a constant resistance to motion of 100 N.

To find the braking force acting on the car, we can use the principles of physics, specifically the equations of motion and Newton's second law. Let's break down the problem step by step.

Understanding the Problem

We have a car with a mass of 1 tonne (which is equivalent to 1000 kg) that is initially traveling at a speed of 40 m/s. The car comes to a complete stop over a distance of 80 m. Additionally, there is a constant resistance to motion, such as friction, which is given as 100 N. Our goal is to determine the braking force applied to the car.

Using the Equations of Motion

First, we can use the equation of motion that relates initial velocity, final velocity, acceleration, and distance:

• v² = u² + 2as

Where:

• v = final velocity (0 m/s, since the car comes to rest)
• u = initial velocity (40 m/s)
• a = acceleration (which we need to find)
• s = distance (80 m)

Plugging in the values:

• 0 = (40)² + 2a(80)

This simplifies to:

• 0 = 1600 + 160a

Now, solving for acceleration (a):

• 160a = -1600
• a = -10 m/s²

Calculating the Net Force

Next, we can apply Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:

• F_net = m * a

Substituting the values we have:

• F_net = 1000 kg * (-10 m/s²) = -10000 N

The negative sign indicates that the force is acting in the opposite direction of the motion, which is expected for a braking force.

Finding the Braking Force

The net force acting on the car is the result of the braking force minus the resistance force. We can express this relationship as:

• F_net = F_braking - F_resistance

We know that:

• F_net = -10000 N
• F_resistance = 100 N

Now we can rearrange the equation to find the braking force:

• -10000 N = F_braking - 100 N

Solving for F_braking gives us:

• F_braking = -10000 N + 100 N = -9900 N

Final Result

The braking force applied to the car is 9900 N in the direction opposite to the motion. This force is necessary to bring the car to a stop over the specified distance, taking into account the constant resistance to motion.