When can we use the three equations of motion?

The three equations of motion (v = u + at; s = ut + ½at²; v² = u² + 2as) are valid ONLY when: (1) the motion is along a straight line, (2) acceleration is uniform (constant in magnitude and direction). They cannot be applied to variable acceleration or curvilinear motion.

What is the value of g and how does it affect free fall?

g = 9.8 m/s² (approximately 10 m/s² for board exams) directed downward. For free fall: all objects regardless of mass fall with the same acceleration g (in absence of air resistance). A body dropped from rest (u=0) has velocity v = gt and falls a distance h = ½gt².

What is the formula for displacement in the nth second?

Displacement in the nth second = sₙ = u + a(2n−1)/2. This is derived by subtracting distance in (n−1) seconds from distance in n seconds: sₙ = (un + ½an²) − (u(n−1) + ½a(n−1)²) = u + a(2n−1)/2.

Equations of Motion

Motion in a Straight Line • Class 11 Physics • NCERT • CBSE

The three equations of motion for uniform acceleration are: v = u + at; s = ut + ½at²; v² = u² + 2as. These relate initial velocity (u), final velocity (v), acceleration (a), displacement (s), and time (t) for uniformly accelerated motion.

Key Formulas

v = u + at
s = ut + ½at²
v² = u² + 2as
sₙ = u + a(2n−1)/2
h = ½gt² (free fall from rest)

Frequently Asked Questions

When can we use the three equations of motion?: The three equations of motion (v = u + at; s = ut + ½at²; v² = u² + 2as) are valid ONLY when: (1) the motion is along a straight line, (2) acceleration is uniform (constant in magnitude and direction). They cannot be applied to variable acceleration or curvilinear motion.
What is the value of g and how does it affect free fall?: g = 9.8 m/s² (approximately 10 m/s² for board exams) directed downward. For free fall: all objects regardless of mass fall with the same acceleration g (in absence of air resistance). A body dropped from rest (u=0) has velocity v = gt and falls a distance h = ½gt².
What is the formula for displacement in the nth second?: Displacement in the nth second = sₙ = u + a(2n−1)/2. This is derived by subtracting distance in (n−1) seconds from distance in n seconds: sₙ = (un + ½an²) − (u(n−1) + ½a(n−1)²) = u + a(2n−1)/2.

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