Motion Matrix Worksheet
MOTION MATRIX
Physics Dynamics & Kinematics Practice
NAME:
DATE:
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Velocity
\( v = \frac{\Delta d}{\Delta t} \)
Unit: m/s
Acceleration
\( a = \frac{v_f - v_i}{t} \)
Unit: m/s²
Force
\( F = ma \)
Unit: N
Momentum
\( p = mv \)
Unit: kg·m/s
I. Matrix Fundamentals
1. A 1,200 kg vehicle is traveling at a constant velocity of 25 m/s. Calculate the car's momentum.
2. A sprinter accelerates from rest to a speed of 9.5 m/s in exactly 3.2 seconds. What is the sprinter's average acceleration?
3. How much force is required to accelerate a 0.5 kg football at a rate of 40 m/s²?
4. A bowling ball has a momentum of 35 kg·m/s. If the ball is moving at 5 m/s, what is its mass?
II. Complex Interactions
Break down your multi-step calculations clearly.
5. A 0.15 kg baseball is thrown toward a batter at 40 m/s. The batter hits the ball, reversing its direction and sending it back at 50 m/s. If the impact lasts 0.02 seconds, calculate:
(a) The change in momentum (Δp) (b) The average force applied by the bat
(a)
(b)
6. A rocket with a mass of 50,000 kg is launched. The engines produce a constant thrust (force) of 750,000 N.
(a) Calculate the acceleration of the rocket. (b) How fast will it be going after 10 seconds (vf)?
(a)
(b)
7. A 2.5 kg brick falls from a ledge. Gravity accelerates it at 9.8 m/s². It hits the ground after 1.5 seconds.
(a) What is the brick's final velocity before impact? (b) What is its momentum just before it hits the ground?
(a)
(b)
The Momentum Challenge
A 0.5 kg remote-controlled car is moving at 4 m/s. A force of 2.0 N is applied in the same direction for 3 seconds. What is the new momentum of the car? (Hint: Find acceleration first).
Motion Matrix Answer Key
Answer Key
Motion Matrix • Physics Dynamics
TEACHER COPY
Full Solutions & Key Concepts
I. Matrix Fundamentals
1. Momentum of 1,200 kg car at 25 m/s
p = mv = (1,200)(25) = 30,000 kg·m/s
2. Sprinter acceleration (0 to 9.5 m/s in 3.2s)
a = Δv/t = (9.5-0)/3.2 = 2.97 m/s2
3. Force for 0.5 kg ball at 40 m/s2
F = ma = (0.5)(40) = 20.00 N
4. Mass for p=35 and v=5
m = p/v = 35/5 = 7.00 kg
II. Complex Interactions
5. Baseball Impact (Directional change!)
(a) Δp = m(vf - vi) = 0.15(50 - (-40)) = 0.15(90) = 13.50 kg·m/s
(b) F = Δp/t = 13.5/0.02 = 675.00 N
Note: Directions are opposite; Δv is 90 m/s.
6. Rocket Dynamics
(a) a = F/m = 750,000/50,000 = 15.00 m/s2
(b) vf = vi + at = 0 + (15)(10) = 150.00 m/s
7. Falling Brick
(a) vf = vi + at = 0 + (9.8)(1.5) = 14.70 m/s
(b) p = mv = (2.5)(14.7) = 36.75 kg·m/s
The Momentum Challenge Solution
1. Solve for accel: a = F/m = 2.0 / 0.5 = 4.0 m/s2
2. Solve for final velocity: vf = vi + at = 4 + (4)(3) = 16.0 m/s
3. Solve for final momentum: p = mv = (0.5)(16) = 8.00 kg·m/s
Alt Method: Impulse Theorem → pf = pi + Ft = (0.5)(4) + (2)(3) = 8.00 kg·m/s.
Motion Matrix Slides
MOTION MATRIX
Velocity • Acceleration • Force • Momentum
The Core Variables
Velocity (v)
v = Δd / Δt
Unit: m/s
Acceleration (a)
a = Δv / Δt
Unit: m/s²
Force (F)
F = ma
Unit: Newtons (N)
Momentum (p)
p = mv
Unit: kg·m/s
How they connect
MASS
F = ma
ACCEL.
MASS
p = mv
VELOCITY
Multi-step problems often require you to find acceleration or velocity first.
Guided Practice
A 1,500 kg car speeds up from 10 m/s to 30 m/s in 5 seconds.
Step 1: Acceleration
a = (30 - 10) / 5
a = 4 m/s²
Step 2: Net Force
F = (1,500) × (4)
F = 6,000 N
