## Pages   # Brooklyn Physics help

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#### Practice Exam: Vectors, Motion

1. Vector A: AX=0N; AY=3N; AZ=0N;
Vector B: BX=0m; BY=0m; BZ=4m;
C = A x B;
CX=?
CY=?
CZ=?
|C| = ?
Symbol | . | means the absolute value or the magnitude
What is the angle between the vector A and the vector B?
What is the angle between the vector C and the vector A?
What is the angle between the vector C and the vector B?

2. Vector A: AX=0N; AY=3N; AZ=0N;
Vector B: BX=0m; BY=0m; BZ=4m;
c = AB = ?
What is the angle between the vector A and the vector B?

3. Vector A: AX=0m; AY=3m; AZ=0m;
Vector B: BX=0m; BY=0m; BZ=4m;
C = A + B;
CX=?
CY=?
CZ=?
|C| = ?
What is the angle between the vector A and the vector B?

4. Vector A: AX=0m; AY=3m; AZ=0m;
Vector B: BX=0m; BY=0m; BZ=4m;
C = AB;
CX=?
CY=?
CZ=?
|C| = ?
What is the angle between the vector A and the vector B?

5. Vector A: AX=0N; AY=0N; AZ=3N;
Vector B: BX=0m; BY=4m; BZ=0m;
C = A x B;
CX=?
CY=?
CZ=?
|C| = ?
What is the angle between the vector A and the vector B?

6. Vector A: AX=0N; AY=0N; AZ=3N;
Vector B: BX=0m; BY=0m; BZ=4m;
c = AB = ?
What is the angle between the vector A and the vector B?

7. Vector A: AX=3N; AY=4N; AZ=0N;
Vector B: BX=0m; BY=0m; BZ=5m;
What is the angle between the vector A and the vector B?

8. Vector A: AX=3N; AY=4N; AZ=5N;
Vector B: BX=6m; BY=8m; BZ=10m;
C = A x B;
CX=?
CY=?
CZ=?
|C| = ?
What is the angle between the vector A and the vector B?

9. Vector A: AX=3N; AY=4N; AZ=0N;
m=2 kg;
C = A / m;
CX=?
CY=?
CZ=?
|C| = ?
What is the angle between the vector C and the vector A?

10. The initial position of a free falling body: X=0m; Y=20m; Z=0m.
Y-axis is directed vertically up. Y=0m is the ground level.
The initial velocity is V: VX=4 m/s; VY=10 m/s; VZ=3 m/s.
Use g=10m/s2
a) VF is the final velocity of the free falling body just before it collide the ground (Y=0).
VFX = ?
VFY = ?
VFZ = ?
b) VA is the average velocity for the total falling time?
VAX = ?
VAY = ?
VAZ = ?
c) What is the distance between the starting, initial point and the final, ground level point?
d) Write mathematical operation in form of some Calculus expression, which allow to calculate the average speed for this problem. It is not necessary to solve this expression.

11. Let we know:
a) the initial position x0=1m of some material point in the X-axis,
b) the initial speed V0 X= 2m/s of this point, and
c) the acceleration aX of this point depend on time as: aX=3m/s3×t, where time t is in seconds.
Find position x(t) and velocity VX(t) of this material point as functions of time t.
Find the velocity of this material point VX(x) as a function of coordinate x.

12. Let we know
a) the initial position x0=1m of some material point in the X-axis,
b) the initial speed V0 X= 2m/s of this point, and
c) how the acceleration of this point depend on its position x: aX=3/s2 x, where x is in meters.
a) Find the position x(t) of this material point as a function of time t.
b)Find the velocity VX(t) of this material body as a function of time t
c) Find the velocity VX(x) of this material body as a function of coordinate x

13. A material point traveling in a circle with a constant speed of 6 m/s has a centripetal acceleration of 2 m/s2 . What is the radius of the circle?

14. A free falling body A is released from the rest.
A free falling body B is released at the same time however with the initial horizontal
velocity of 4 m/s.
a) What are speeds of the falling bodies A and B after 0.3 s (Use g=10 m/s2)?

VA=
VB
=

1. A free falling body A is released from the rest.
A free falling body B is released at the same time however with the initial vertical
velocity of 4 m/s up.
a) What are speeds of the falling bodies A and B after 0.3 s (Use g=10 m/s2)?

VA=
VB=

b) What will be the distance between the falling bodies A and B after 0.3 s (Use g=10m/s)?

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