# Need to find Stopping Distance [closed]

I'm given these following.

• Mass of the car $$= 1800 \text{ kg}$$
• Friction coefficient $$= 0.6$$
• Velocity $$= 8.3 \text{ m}/\text{s}$$

I need to find the stopping distance and deceleration using this and I have no idea how.

Step 1: Draw a free body diagram.

In a free body diagram, you visually represent every force acting on the body by arrows. The arrows point along the direction of the force. A free body diagram is not necessary. But it would help you to visualize the direction of the forces and direction of motion of the body.

You should note that frictional force keeps acting on the body as long as there is relative motion between the surface and the body, i.e. friction force tries to prevent relative motion. It's magnitude too is constant for the entire duration as friction depends only on nature of contact surfaces and the normal force on the body.

Also note that normal force always acts upward and perpendicular to the plane of motion. Normal force can be explained by Newton's third law: since body exerts a weight $$mg$$ on the surface, the surface too exerts an equal and opposite force $$N$$ on the body.

Step 2: Find the magnitude of the acceleration of the body due frictional force acting on it.

Here,

$$f=\mu N$$, where $$f,\mu$$ and $$N$$ represent dynamic friction, coefficient of dynamic friction and normal force.

Using Newton's Second Law, equate:

In vertical direction:

$$F_{net}=ma_{net}$$

$$\Rightarrow N-mg=m.0$$ (net acceleration in vertical direction is $$0$$, and $$N$$ and $$mg$$ are in opposite direction)

$$\\ \\ \Rightarrow N=mg \\$$

In horizontal direction:

$$F_{net}=ma_{net}$$

$$\Rightarrow f=\mu N=ma_{net}$$

Now isolate $$a_{net}$$

Step 3: Use the appropriate equation of motion. You now have the initial speed $$u$$, final speed $$v$$ and acceleration $$a$$. You require time. So select the appropriate equation of motion and substitute the values you have. And most importantly, use the sign system properly.

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• This is a well structured, informative, and general answer for solving these types of exercises. Oct 29, 2020 at 1:20