Question

A car weighing 9800 N is moving with a speed of 50 km./h.On the application of the brakes it comes to rest after travelling a distance of 60m .Calculate the average retarding force.

Answer 1

Answer on Question 71466, Physics, Mechanics, Relativity

Question:

A car weighing $9800\,N$ is moving with a speed of $50\,km/h$. On the application of the brakes it comes to rest after travelling a distance of $60\,m$. Calculate the average retarding force.

Solution:

We can find the average retarding force from the Newton's Second Law of Motion:

$$F_{avg} = ma,$$

here, $F_{avg}$ is the average retarding force acting on the car, $m$ is the mass of the car, $a$ is the acceleration of the car.

We can find acceleration from the kinematic equation:

$$v^2 = v_0^2 + 2ad,$$

here, $v_0$ is the initial velocity of the car, $v = 0$ is the final velocity of the car (when it comes to rest), $a$ is the acceleration of the car and $d$ is the distance travelling after application of the brakes.

Then, we get:

$$a = -\frac{v_0^2}{2d}.$$

Let's first convert $km/h$ to $m/s$:

$$v_0 = 50 \frac{km}{h} \cdot \frac{1000\,m}{1\,km} \cdot \frac{1\,h}{3600\,s} = 13.9 \frac{m}{s}.$$

Then, we can substitute $v_0$ into formula for acceleration and calculate it:

$$a = -\frac{v_0^2}{2d} = -\frac{\left(13.9 \frac{m}{s}\right)^2}{2 \cdot 60\,m} = -1.61 \frac{m}{s^2}.$$

The sign minus indicates that the car decelerates.

Also, we can find the mass of the car from the definition of the weight:

$$W = m g,$$ $$m = \frac {W}{g} = \frac {9 8 0 0 N}{9 . 8 \frac {m}{s ^ {2}}} = 1 0 0 0 k g.$$

Finally, we can find the average retarding force:

$$F _ {a v g} = m a = 1 0 0 0 k g \cdot \left(- 1. 6 1 \frac {m}{s ^ {2}}\right) = - 1 6 1 0 N.$$

The sign minus indicates that the average retarding force directed in the opposite direction to the motion of the car.

**Answer:**

$$F _ {a v g} = 1 6 1 0 N.$$

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