Mechanics (Physics)
What is the SI unit of force
Newton
What is the SI unit of electric current?
Ampere
What is the value of x if 2x + 3 = 7
x = 2
What is the derivative of x²?
2x
What is the magnitude of vector A = 3i + 4j?
5 (√(3² + 4²))
A body moves with a constant speed in a circular path. Is it accelerating?
yes, because the direction is changing
What is Ohm’s Law?
V = IR (Voltage = Current × Resistance)
What is (a + b)² equal to
a² + 2ab + b²
Find the integral of x dx.
(1/2)x² + C
If two vectors are perpendicular, what is their dot product?
0
State Newton's Second Law of Motion
Force = mass × acceleration (F = ma)
A 12V battery is connected to a 4Ω resistor. Find the current.
3 A
Find the roots of the equation x² - 5x + 6 = 0
x = 2 and x = 3
What is the derivative of sin(x)
cos(x)
Angle between two equal vectors is 60°. Find the dot product if |A| = 5
25 × cos(60°) = 12.5
A projectile reaches maximum height in 2 seconds. What is the total time of flight?
4 seconds?
Define electric power in terms of current and resistance.
P = I²R
Solve: log(x²) = 2 log(x)
x ≠ 0 (identity holds for all x ≠ 0)
If y = e^x, then dy/dx = ?
e^x
What is the formula for the distance between two points (x₁, y₁) and (x₂, y₂)
√[(x₂ - x₁)² + (y₂ - y₁)²]
A car accelerates from rest at 3 m/s² for 5 seconds. Find its final speed.
15 m/s
Two resistors of 6Ω and 3Ω are connected in parallel. What is the total resistance?
2Ω
If f(x) = x² + 1, find f(2x)
4x² + 1
Find the area under the curve y = x between x = 0 and x = 2.
2 (∫₀² x dx = (1/2)(2²) = 2)
Find the angle between vectors A = i + j and B = i – j.
90°