Atruck is going 30 m/s when the driver applies the brakes for 4.7 s so that the truck slows down to 20 m/s. a) what is the acceleration of the truck? b) how far does the truck go during the 4.7 s?

Answer :

(a) The acceleration of the truck is,

(b) The distance covered by the truck is, 117.8 m

Explanation :  

By the 1st equation of motion,

...........(1)

where,

v = final velocity = 20 m/s

u = initial velocity  = 30 m/s

t = time = 4.7 s

a = acceleration of the truck = ?

Now put all the given values in the above equation 1, we get:

The acceleration of the truck is,

By the 2nd equation of motion,

...........(2)

where,

s = distance covered by the truck = ?

u = initial velocity  = 30 m/s

t = time = 4.7 s

a = acceleration of the truck =

Now put all the given values in the above equation 2, we get:

By solving the term, we get:

The distance covered by the truck is, 117.8 m

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.