Calculating Overall Distance: Solving for S1 in a Two-Part Motion Problem

[skp123]

Homework Statement

A spots car reaches the speed V₁ = 100 km/h within 5 sec. At that speed, its breaking distance
is S₂ = 40 m.
a) What is the overall distance S covered by the car?

Homework Equations

V=V₀ + at

S=S₀ + V₀t + 1/2a₁t²

Overall distance = S₁ + S₂

The Attempt at a Solution

I'm having trouble calculating the time and calculating S₁. We know that S₂ = 40. How to calculate S₁

 

[Doc Al]

I presume S₁ is the distance covered as it accelerates to the given speed? The equations you have are just what you need. Find the acceleration, then use it to find the distance. (Be sure to convert the speed to standard units--m/s.)

 

[skp123]

Yes - S1 is the distance covered as it accelerates to the given speed .

OK the acceleration is a₁ = V₁ / t₁ = 100/5 = 20

And now we have S₁=1/2a₁t²

How to find the time - t ? And by the way velocity is uniformly accelerated

 

[Doc Al]

OK the acceleration is a₁ = V₁ / t₁ = 100/5 = 20

No. You first need to convert the speed to standard units. Then your equation will work fine.

And now we have S₁=1/2a₁t²

How to fing t ?

The time is given. (You just used it to find the acceleration!)

 

[skp123]

Ok . Can you tell me how to convert the speed to standard units.

 

[Doc Al]

Ok . Can you tell me how to convert the speed to standard units.

100 km = ? meters
1 hr = ? seconds

Divide!

(Or use Google to do the conversion for you. )

 

[skp123]

Ohh yeah. So a₁ = V₁ / t₁ = 100/3.6 * 1/5 = 5.5 .
Correct ?

 

[Doc Al]

Ohh yeah. So a₁ = V₁ / t₁ = 100/3.6 * 1/5 = 5.5 .
Correct ?

Not yet.

$$\frac{100 km}{hr} \times \frac{? m}{km} \times \frac{hr}{? s} =$$

Fill in the quesion marks so that each of the two "conversion factors" equals 1. How many meters in one km? How many seconds in an hour?

 

[skp123]

OK. 1km=1000m and 1hr = 3600s.

So 100 km/h = 27.7 m/s

 

[ideasrule]

Yeah. Notice that this is equivalent to dividing 100 km/h by 3.6.