Given a particle that has the acceleration a(t) = 4e3 meters, a. find the displacement at 2 seconds, assuming an initial position of o & from rest. b. find velocity at 1 second assuming starting from rest.

Hi!

The acceleration of our particle is then a = 4* meters per second square. Also we know that we start at X₀ = O m (i am not sure if you are using a a 0 or a O, but you will see that in this problem it doesn't matter, se i will use a constant O, that can be  ani real number as the initial position) and V₀ = 0 m/s.

Ok, we have the acceleration, so if we want the velocity, we must integrate the acceleration over time.

V(t) = ∫ 4*dt = 4**t + V₀

where we added the constant of integration, who is the inicial velocity, that we already know that is zero.

and for the position, we must integrate again.

X(t) =  ∫ 4**tdt =  4**/2 + X₀

ok, in the part a) we want to know the displacement at 2 seconds.

that is X(2s) - X(0s) = (2000*4 + O) - O meters = 8000 meters.

in the b part we want to know the velocity at 1 second; that is:

V(1s) = 4000*1 m/s = 4000 meters per second.

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles