Question

A displacement vector is given:

r=(2.3m) i hat +(5.4m/s^2) t^2 j hat- (3.0m/s^3) t^3 z hat

a.   Find the displacement from t=0 s to t=3.0 s.

b.   Find the velocity vector.  

c.   Find the average velocity from t = 0 s to t = 3.0 s.

d.   Find the acceleration vector.

Answer 1

Here .

r = 2.3 i + (5.4 t^2 ) j - 3 t^3 k

a)

displacement from 0 to 3 s

displacement = 2.3 i + (5.4 3^2 ) j - 3 3^3 k - 2.3 i

displacement = 48.6 i - 81 j m

the displacement is 48.6 i - 81 j m

b)

velocity = dr/dt

velocity = d/dt(2.3 i + (5.4 t^2 ) j - 3 t^3 k)

velocity = 10.8 t j - 9 t^2 k m/s

c)

avearge velocity = displacement/time

average velocity = ( 48.6 i - 81 k m )/3

average velocity = 16.2 i - 27 k m/s

d)

acceleration = dv/dt

acceleration = d/dt( 10.8 t j - 9 t^2 k)

a = 10.8 j - 18 * t k m/s^2