- #1

rudransh verma

Gold Member

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- Homework Statement:
- A car starts from rest to cover a distance s. mu is coefficient of friction between road and tyre. The minimum time in which the car covers the distance is proportional to :

- Relevant Equations:
- ##F=ma##

Since the car starts from rest it’s accelerating. So, $$F_a-f_k=ma$$

$$F_a-\mu mg=ma$$

$$\frac{F_a-\mu mg}m=a$$

Now from second eqn, ##s=ut+\frac12at^2##

$$s=\frac12\frac{F_a-\mu mg}mt^2$$

$$\frac{2sm}{F_a-\mu mg}=t^2$$

$$\sqrt{\frac{2sm}{F_a-\mu mg}}=t$$

I don’t think I am getting any where!

$$F_a-\mu mg=ma$$

$$\frac{F_a-\mu mg}m=a$$

Now from second eqn, ##s=ut+\frac12at^2##

$$s=\frac12\frac{F_a-\mu mg}mt^2$$

$$\frac{2sm}{F_a-\mu mg}=t^2$$

$$\sqrt{\frac{2sm}{F_a-\mu mg}}=t$$

I don’t think I am getting any where!

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