Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = t i + t2 j + 3 k v(t) = a(t) = sketch the path of the particle and draw the velocity and acceleration vectors for t = 1.

Velocity

v= i + 2  j

Acceleration

a= 2 j

Explanation:

Given that

r(t) = t i + t² j + 3 k

We know that

Velocity v given as

v= dr/dt

dr/dt= i + 2 t j +0

v= i + 2 t j

At t= 1

v= i + 2 x 1 j

v= i + 2  j

Acceleration ,a

a=  dv/dt

v= i + 2 t j

dv/dt= 2 j

a= 2 j

that would be b i just took the test : )

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