Aprofessional race-car driver buys a car that can accelerate at 5.2 m/s2 . the racer decides to race against another driver in a soupedup stock car. both start from rest, but the stock-car driver leaves 1.3 s before the driver of the sports car. the stock car moves with a constant acceleration of +3.2 m/s2 . find the time it takes the sports-car driver to overtake the stock-car driver. answer in units of s.

6.02 s

Explanation:

We can write the position of the stock car as:

where

is the acceleration of the stock car.

The sport car instead starts its motion only 1.3 s afterwards, therefore its position at time t can be written as

where

is the acceleration of the sport car

(we can verify indeed that when t = 1.3 s, ).

The sport car reaches the stock car when the two positions are equal:

Rewriting the equation,

This is a second-order equation with two solutions:

t = 0.73 s

t = 6.02 s

We discard the first solution since we are only interested in the times > 1.3 s, therefore the sport car overcomes the stock car after

6.02 seconds.

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s