1
Newton’s Second Law and Circular Motion- HW Problems
1. Find the velocity and acceleration vectors and the speed for
1 2 1 3 2 3
𝑐⃗(𝑡) = ( 𝑡 )𝑖⃗ + ( 𝑡 )𝑗⃗ + ( 𝑡 2 )𝑘⃗⃗.
2 3 3
2. Determine which of the following curves is regular.
a. 𝑐⃗(𝑡) =< cos(2𝑡) , sin(2𝑡) , 𝑡 >
b. 𝑐⃗(𝑡) =< cos(𝑡 2 ) , sin(𝑡 2 ) , 𝑡 2 >
c. 𝑐⃗(𝑡) =< 𝑒 𝑡 , 𝑡 4 , 2𝑡 + 1 >
3. The acceleration, initial velocity, and initial position of a particle is
given by 𝑎⃗(𝑡) =< −4, 12𝑡, 2 > , 𝑣⃗ (0) =< −4, 6, −6 > ,
𝑟⃗(0) =< 0, 0, 5 > . Find the particle’s path 𝑟⃗(𝑡) and when it crosses
the 𝑥-𝑦 plane.
4. A body of mass 6 kg moves in a circle of radius 3 m making one
revolution every 4 seconds. Find the centripetal force on the body.
2
5. The velocity of a particle is given by 𝑣⃗(𝑡) =< 𝑡𝑒 𝑡 , 2𝑡, 3𝑡 2 + 1 > .
Find the path of the particle, 𝑐⃗(𝑡), if 𝑐⃗(0) =< 2, 3, 4 >.
Newton’s Second Law and Circular Motion- HW Problems
1. Find the velocity and acceleration vectors and the speed for
1 2 1 3 2 3
𝑐⃗(𝑡) = ( 𝑡 )𝑖⃗ + ( 𝑡 )𝑗⃗ + ( 𝑡 2 )𝑘⃗⃗.
2 3 3
2. Determine which of the following curves is regular.
a. 𝑐⃗(𝑡) =< cos(2𝑡) , sin(2𝑡) , 𝑡 >
b. 𝑐⃗(𝑡) =< cos(𝑡 2 ) , sin(𝑡 2 ) , 𝑡 2 >
c. 𝑐⃗(𝑡) =< 𝑒 𝑡 , 𝑡 4 , 2𝑡 + 1 >
3. The acceleration, initial velocity, and initial position of a particle is
given by 𝑎⃗(𝑡) =< −4, 12𝑡, 2 > , 𝑣⃗ (0) =< −4, 6, −6 > ,
𝑟⃗(0) =< 0, 0, 5 > . Find the particle’s path 𝑟⃗(𝑡) and when it crosses
the 𝑥-𝑦 plane.
4. A body of mass 6 kg moves in a circle of radius 3 m making one
revolution every 4 seconds. Find the centripetal force on the body.
2
5. The velocity of a particle is given by 𝑣⃗(𝑡) =< 𝑡𝑒 𝑡 , 2𝑡, 3𝑡 2 + 1 > .
Find the path of the particle, 𝑐⃗(𝑡), if 𝑐⃗(0) =< 2, 3, 4 >.
