Question

HELP PLEASE Assuming equal rates of acceleration in both cases, how much farther would you travel if

braking from 56 mi/h to rest than from 28 mi/h
a 3.2 times farther
b 4.8 times farther
c 4.0 times farther
d 5.2 times farther

Answer 1

(c) is the correct option.

Step-by-step explanation:

Given that,

Initial velocity, u = 56 mi/h and 28 mi/h

Final velocity, v = 0

It is coming to rest it means it is under deceleration. So, it will be (-a). Using the third equation of motion as folows :

`v^2-u^2=2as`

So,

`0-(56)^2=2(-a)* s\\\\s=(3136)/(2a)\\\\s=(1568)/(a)\ ....(1)`

Also,

`0-(28)^2=2(-a)* s'\\\\s'=(784)/(2a)\\\\s'=(392)/(a)\ ....(2)`

Dividing equation (1) by (2)

So,

`(s)/(s')=((1568)/(a))/((392)/(a))\\\\\text{s is same for both cases}\\\\(s)/(s')=4\\\\s=4* s'`

So, we will travel 4 times farther if braking from 56 mi/h to rest than from 28 mi/h.