Question

You're driving down the highway late one night at 20m/s when a deer steps onto the road 47 m in front of you. Your reaction time before stepping on the brakes is 0.50s, and the maximum deceleration of your car is 10m/s2. A) Part complete How much distance is between you and the deer when you come to a stop? Express your answer to two significant figures and include the appropriate units. B)What is the maximum speed you could have and still not hit the deer? Express your answer to two significant figures and include the appropriate units.

Answer 1

here,

the initial speed , u = 20 m/s

s = 47 m

maximum accelration , am = 10 m/s^2

a)

t1 = 0.5 s

the distance travelled in t1 , s1 = u * t1

s1 = 10 m

after break applied

the distance travelled befpre stopping , s2 = u^2 /2a

s2 = 20^2 /( 2 * 10) m

s2 = 20 m

so, the distance between deer and us , s3 = s - s1 - s2

s3 = 17 m

b)

let the maximum initial speed be u

t1 = 0.5 s

the distance travelled in t1 , s1 = u * t1

after break applied

the distance travelled befpre stopping , s2 = u^2 /2a

for maximum initial speed

s = s1 + s2

47 = u * t1 + u^2 /2a

47 = u * 0.5 + u^2 /( 2 * 10)

solving for u

u = 26.1 m/s

the maximum initial speed is 26.1 m/s