Physics acceleration question???????

Question

Coasting due west on your bicycle at 8.4 m/s, you encounter a sandy patch of road 8.2 m across. When you leave the sandy patch your speed has been reduced by 3.1 m/s to 5.3 m/s.

(a) Assuming the sand causes a constant acceleration, what was the bicycle's acceleration in the sandy patch? Give both magnitude and direction.

Answer 1

<<  what was the bicycle's acceleration in the sandy patch? >>

Your working formula is

Vf^2 - Vo^2 = 2as

where

Vf = final velocity = 5.3 m/sec

Vo = initial velocity = 8.4 m/sec.

a = acceleration along the sandy patch

s = length of the sandy patch = 8.2 m

Substituting appropriate values,

5.3^2 - 8.4^2 = 2(a)(8.2)

Solving for "a",

a = (5.3^2 - 8.4^2)/(2 * 8.2)

a = -2.59 m/sec^2

NOTE -- the negative sign indicates that the bicycle was actually decelerating while negotiating the sandy patch.

<< How long did it take to cross the sandy patch? >>

Working formula is

Vf - Vo = aT

where

T = time to cross the sandy patch

while all other terms have been previously defined.

Substituting terms,

5.3 - 8.4 = (-2.59)T

Solving for T,

T = (5.3 - 8.4)/(2.59)

T = 1.2 seconds

<<  Suppose you enter the sandy patch with a speed of 9.4 m/s. Is your final speed in this case equal to, more than, or less than 6.3 m/s? >>

Use the same formula

Vf^2 - Vo^2 = 2as

and assuming all acceleration to be the same, then

Vf^2 - 9.4^2 = 2(-2.59)(8.2)

Vf^2 = 9.4^2 - 2(-2.59)(8.2)

Vf = 6.77 m/sec.

Therefore, if the inital velocity of the bike entering the sandy patch were 9.4 m/sec, then its exit velocity is greater than 6.3 m/sec.

Answer 2

use the formula

v^2 = u^2 + 2as

where v is the final velocity (5.3 m/s)

u= initial velocity (8.4 m/s)

a= acceleration

s= distance ( 8.2 meters)

plot in the number and a will be your magnitude, and if the answer is negative then its deceleration.

For the second part use the formula

v=u+at

where t is the time in seconds. so just substitute in the values that you have from the question and use the answer for acceleration that you got from the first part.

and for the last part of the question, just use the above formulas and substitute in the values for v ( as your new final velocity) and u ( as your new initial velocity). So try the 6.3 m/s once and the second time a value higher and a third time a value lower.

hope you understood it.