Find the acceleration?

Question

A driver in a car traveling at a speed of 60 mi/h sees a deer 80 m away on the road. Calculate the minimum constant acceleration that is necessary for the car to stop without hitting the deer (assuming that the deer does not move in the meantime).

Answer 1

poor deer.....
helo!
well you must first know that
1Mile = 1600m!
and
1h=3600sec
so 60mi/h=60*1600/3600m/s=60*16/36m/s=10*16/6m/s=160/6m/s=
80/3m/s=27m/s

u=uo-at
where u=0 , uo=27m/s
=> uo=at=> 27=at => t=27/a

x=uo*t-at^2/2=at^2/2
where x=80

80=a(27/a)^2/2

160a=80*80/9=>
2a=80/9
a=40/9
a=4m/sec^2


ok?
have a nice day!

Answer 2

Vf^2 - Vi^2 = 2*A*(distance traveled)
Vf = final velocity = zero (since car is stopping)
Vi = initial velocity = 60 mi/h (but convert to m/s before plugging in)
distance traveled = 80 m
A = acceleration
That equation is always true when acceleration is constant. Plug in the numbers you know and you'll get the acceleration!

Answer 3

14.75 feet per second per second (directed from the deer toward the car; or a negative acceleration if you're looking from the car toward the deer)

This presupposes that you're accurately posing the car speed as 60 miles per hour (=88 feet per second) and the distance as 80 METERS (converted to 262.47 feet) from the car to the deer at the instant you want to get your info.

(Catarther (sp?) is all right till his/her last equation 80 = ... and he/she introduced some minor rounding error with conversion to metric units: 60 mph = 26.82 m/sec. You will also note that 14.75 feet is abt the same as 4.5 meters.)

Answer 4

1st let's convert to meters:
60 mi/h = 1.6 * 60 000 m/3600 s = 26.7 m/s.

So the car has to go from 26.7m/s to 0 m/s in 80m.

using
v = at +vo
0 = at + 26.7
t = -26.7/a

and
d = 1/2 at^2 + vot
80 = 1/2 a (-26.7/a)^2 + 26.7 (-26.7/a)
80 = 712.89/2a - 712.89/a = -712.89/a

a = -712.89/80 = 8.9 m/s^2

Answer 5

let´s take coherent units 60mi/h =26.822m/s

v=@t+v_o and space = 1/2@t^2 +v_o*t
v must be 0 so t=-v_o/@ and space must be 80m

so 80= 1/2*@ *v_o^2 /@^2 -v_o^2/@ 80= -1/2v_o^2 */@

@= -1/2 *v_o^2 /8o m/s^2= -4.5 m/s^2