- #1

Physics_is_beautiful

- 13

- 1

- Homework Statement
- The question states :

--> A person and a car are in a race together.

-->The runner runs at a constant speed of 10 m/s from the start of The race. During the first 5.0 s of the race, the car's speed increases from 0m/s to 25 m/s at a uniform rate.

then asks :

--> At what point of time does the car over take the runner?

[Same exact words as per question]

- Relevant Equations
- all basic equations of motions,

but particularly :

a = (v-u)/t

s = ut+1/2at^2

here's what I did :

I tried to balance both sides of the equations, to find the point where both the car and the runner are at the same place, thus ;

--> ut + 1/2at^2 = ut + 1/2at^2

--> (10)(t)+1/2(0)(t^2) = (0)(5) + 1/2(5)(t^2)

[ Here LHS if for the runner, RHS for the car. I do realise that the speed of a human cannot be 0 right at the start, as in, he needs to accelerate due to inertia, but the question states that he's at 10 m/s from the start, so T = 0.0s is a point in time where the speed of the car = 0 m/s and the the speed of the person in 10m/s]

-->10t = 2.5t^2

--> 4t = t^2

--> t = 4 s

However, the question asks specifically at what point in time does the car overtake the runner, which is Immediately after t = 4.0s.

But, when exactly?

since the time is given to 2 sig-figs, I gave the answer as approx 4.1s, but I am not too sure of that.

That's where I need help.

Thanks.

I tried to balance both sides of the equations, to find the point where both the car and the runner are at the same place, thus ;

--> ut + 1/2at^2 = ut + 1/2at^2

--> (10)(t)+1/2(0)(t^2) = (0)(5) + 1/2(5)(t^2)

[ Here LHS if for the runner, RHS for the car. I do realise that the speed of a human cannot be 0 right at the start, as in, he needs to accelerate due to inertia, but the question states that he's at 10 m/s from the start, so T = 0.0s is a point in time where the speed of the car = 0 m/s and the the speed of the person in 10m/s]

-->10t = 2.5t^2

--> 4t = t^2

--> t = 4 s

However, the question asks specifically at what point in time does the car overtake the runner, which is Immediately after t = 4.0s.

But, when exactly?

since the time is given to 2 sig-figs, I gave the answer as approx 4.1s, but I am not too sure of that.

That's where I need help.

Thanks.

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