AP PHYSICS HOMEWORK: Could you help me out with this!?

Question

Suppose you are in the front seat of a car traveling 90 km/h as it skids into a tree. The car comes to stop in a distance of 1 meter as the front end crumples around the tree.

- If you are wearing a seat belt, you stop with the same negative acceleration as the car. What is the magnitude of this acceleration?

- If you are not wearing a seat belt, you continue forward at 90 km/h until you hit the dashboard. You are then brought to rest in a distance of about 15 cm as your body crumples against the dashboard. Find the magnitude of the acceleration of your body in this case.

... I got a totally ridiculous answer for the first part; -4,050,000 km/h. Yikes, I know. :( Can anybody help?

Answer 1

1) v^2 = u^2 + 2as

v = 0 s = 1 u = 90,000/3600 m/s

a = -u^2/2s = -(90,000/3600)^2/2

a = 312.5 m/s^2 = 1125km/h^2

b) replace s with 0.15

a = 2083.3 m/s^2 =  7500 km/h^2

Answer 2

First you should convert all the values to the same units.

90 km/h = 90000 / 3600 m/s = 25 m/s

Now use the equation

v^2 = u^2 + 2as

The final speed is 0, and the initial speed 25 m/s, and the distance is 1m, so

a = (v^2 - u^2) / (2s)

= (0 - 25^2) / (2 * 1)

= -312.5 m/s^2

so the magnitude of the acceleration is

313 m/s^2

If you want, you can convert this back to kilometers per hour:

(312.5 / 1000) / (1 / 3600) km/h

= 1125 km/h

= 1130 km/h

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In the second case, the final speed is again 0, and the initial 25m/s, but this time the distance is 15cm = 0.15 m

so the acceleration is

a = (v^2 - u^2) / (2s)

= (0 - 25^2) / (2 * 0.15)

= -2083.3333 m/s^2

So the magnitude of the acceleration int hsi case is

2080 m/s^2

And again you can convert this to kilometers per hour;

= (2083.3333 / 1000) / (1 / 3600) km/h

= 7500 km/h

Answer 3

1st of all you have to use SI units, i.e

90 / 3600 (to get to km per second)

90/3600 * 1000 (to get to metres per second)

this gives 25 metres per second

Thats a standard thing, to go from km/h to m/s divide by 3600 and multiply by 1000

They should have given you, or you will find in ur textbook or whatever the kinematic equations.

The one youre after is -

(Velcity Final)^2 = (Velocity Initial)^2 + 2 * Acceleration * Displacement

Vf^2 = Vi^2 + 2ax

i.e

Velocity Final = 0

Velocity Inital = 25 (m/s)

Acceleration = ?

Displacement = 0.15 (metres)

therefore

0 = 25^2 + 2 * a * 15

625 / (2 * 0.15) = a

a = 2083.33 m/s^2

thats alot of acceleration

(note units for acceleration are metres per second per second)

you probably got a ridiculous answer cause you were using km/h, convert it to m/s (metres per second as mentioned)

therefore

0 = 25^2 + 2 * a * 1

a = 25^2 / (2 * 1)

   = 312.5 m/s^2