Question

A women is wearing her seat belt, while driving at 60km/hr.
She finds it necessary to slam on her brakes and she slows
uniformly to a stop in 1.6 sec. What is the average
acceleration experionced by her?
​

Answer 1

Given: Speed is 60 km/hr and the time taken to stop is 1.6 s.

To find: The average  acceleration experienced.

Solution:

• The initial velocity (u) is 60 km/hr as the woman is driving at that speed.
• The final velocity (v) is 0 km/hr as she slams her brakes and the vehicle comes to rest.
• The time taken for the vehicle to stop is 1.6 s which is 4 × 10⁻⁴ hr.
• According to the one dimensional formula,

        $v = u + at$

        $0 = 60 + (4 * 10^{-4}) a$

        $a = - 15 * 10^{-4} km hr^{-2}$

Therefore, the acceleration experienced is 15 × 10⁻⁴ km hr⁻².

Answer 2

Given : A women is wearing her seat belt, while driving at 60km/hr.

She finds it necessary to slam on her brakes and she slows

uniformly to a stop in 1.6 sec.

To Find :  the average acceleration experienced by her?

Solution:

u = 60 km/hr

= 60 * 1000 / 3600

= 50/3  m/s

a = ?

v = 0   as stops

t = 1.6 secs

v = u + at

=> 0 = 50/3  + a (1.6)

=> -50/3 = 1.6a

=> a = -50/(3 * 1.6)

=> a = - 50/4.8

=> a = -500/48

=> a = -125/12

=> a = -10.4167  m/s²

Finding in km/hr²

u = 60

v = 0

t = 1.6 secs  = 1.6/3600  hr

0 = 60 + a ( 1.6/3600)

=> a (1.6/3600) = - 60

=> a =  -60 * 3600 /1.6

=> a = 135000 km/hr²

=> a = 1.35 * 10⁵ km/hr²  

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