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Work Energy AND Power formulas

Master Work Energy AND Power through 28 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Work Energy AND Power, every formula

28 formulas, typeset and free. Print it, or keep it open beside your practice.

Work by a constant force
$W = F \cdot S = F S cos θ$
Work by a variable force
$W = \int F \cdot d s$
Q1MCQVariable force
The work done by a variable force is:
- A
  $\int\vec F\cdot d\vec s$
- B
  $FS$
- C
  $\dfrac{F}{s}$
- D
  $F+s$
Kinetic energy
$K = \frac{1}{2} m v^{2}$
KE–momentum relation
$K = \frac{p ^{2}}{2 m}$
Q1MCQKE–momentum
Kinetic energy in terms of momentum is:
- A
  $\dfrac{p^{2}}{2m}$
- B
  $\dfrac{p}{2m}$
- C
  $2mp$
- D
  $\dfrac{p^{2}}{m}$
Momentum from KE
$p = 2 m K$
Q1MCQMomentum from KE
The momentum of a body with kinetic energy $K$ is:
- A
  $\sqrt{2mK}$
- B
  $2mK$
- C
  $\dfrac{K}{m}$
- D
  $\sqrt{mK}$
Work–energy theorem
$W_{n e t} = Δ K = K_{f} - K_{i}$
Potential energy
$U = - \int_{\infty}^{r} F \cdot d r = - W$
Q1MCQPotential energy
The potential energy is related to work by a conservative force as:
- A
  $U=-W$
- B
  $U=W$
- C
  $U=2W$
- D
  $U=W^{2}$
Conservative force from PE
$F = - \frac{d U}{d r}$
Q1MCQForce from PE
A conservative force equals:
- A
  $-\dfrac{dU}{dx}$
- B
  $\dfrac{dU}{dx}$
- C
  $U x$
- D
  $-U$
Gravitational PE
$U = m g h$
Elastic (spring) PE
$U = \frac{1}{2} k x^{2}$
Conservation of mechanical energy
$K + U = constant$
conservative forces only
Q1MCQEnergy conservation
When only conservative forces act, the quantity conserved is:
- A
  $K+U$
- B
  $K$ only
- C
  $U$ only
- D
  $K-U$
Change in PE
$Δ U = - W_{c}$
Q1MCQChange in PE
The change in potential energy equals:
- A
  $-W_c$
- B
  $W_c$
- C
  $\Delta K$
- D
  $0$
Average power
$P_{a v g} = \frac{W}{t}$
Instantaneous power
$P = \frac{d W}{d t} = F \cdot v$
Work by gravity
$W = - m g Δ h$
rising
Q1MCQWork by gravity
The work done by gravity on a body rising a height $h$ is:
- A
  $-mgh$
- B
  $+mgh$
- C
  $0$
- D
  $\tfrac12 mgh$
Work by a spring
$W = - \frac{1}{2} k x^{2}$
Q1MCQWork by a spring
The work done by a spring stretched by $x$ is:
- A
  $-\tfrac12 kx^{2}$
- B
  $\tfrac12 kx^{2}$
- C
  $kx$
- D
  $-kx$
Work by friction
$W = - f d$
Stable equilibrium
$\frac{d U}{d x} = 0, \frac{d ^{2} U}{d x ^{2}} > 0$
Q1MCQStable equilibrium
At a point of stable equilibrium:
- A
  $\dfrac{dU}{dx}=0,\ \dfrac{d^{2}U}{dx^{2}}>0$
- B
  $\dfrac{d^{2}U}{dx^{2}}<0$
- C
  $\dfrac{dU}{dx}\neq0$
- D
  $U=0$
Unstable equilibrium
$\frac{d U}{d x} = 0, \frac{d ^{2} U}{d x ^{2}} < 0$
Q1MCQUnstable equilibrium
At a point of unstable equilibrium:
- A
  $\dfrac{d^{2}U}{dx^{2}}<0$
- B
  $\dfrac{d^{2}U}{dx^{2}}>0$
- C
  $\dfrac{d^{2}U}{dx^{2}}=0$
- D
  $U=0$
Neutral equilibrium
$\frac{d U}{d x} = 0, \frac{d ^{2} U}{d x ^{2}} = 0$
Q1MCQNeutral equilibrium
At a point of neutral equilibrium:
- A
  $\dfrac{d^{2}U}{dx^{2}}=0$
- B
  $\dfrac{d^{2}U}{dx^{2}}>0$
- C
  $\dfrac{d^{2}U}{dx^{2}}<0$
- D
  $\dfrac{dU}{dx}\neq0$
Conservative force (curl)
$\nabla \times F = 0$
Q1MCQConservative force curl
A force field is conservative iff:
- A
  $\nabla\times\vec F=0$
- B
  $\nabla\cdot\vec F=0$
- C
  $\vec F=0$
- D
  $\nabla\times\vec F\neq0$
Horsepower
$1 HP = 746 W$
Work as area
$W = area under the F - x graph$
Q1MCQWork as area
The work done by a force from an $F$–$x$ graph is:
- A
  the area under the curve
- B
  the slope
- C
  the peak value
- D
  the x-intercept
KE is non-negative
$K \geq 0$
Q1MCQKE sign
Kinetic energy is always:
- A
  $\ge0$
- B
  $\le0$
- C
  negative
- D
  zero
Modified work–energy theorem
$W_{N C} + W_{P S} = Δ E$
Q1MCQModified WE theorem
For non-conservative and pseudo work, $W_{NC}+W_{PS}$ equals:
- A
  $\Delta E$ (change in total mechanical energy)
- B
  $\Delta K$
- C
  $\Delta U$
- D
  $0$
Power–velocity (constant P)
$P = F v$
Efficiency
$η = \frac{output}{input}$
Work done in a round trip (conservative)
$\oint F \cdot d r = 0$

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Work Energy AND Power formulas

Work Energy AND Power, every formula

Work by a constant force

Work by a variable force

Kinetic energy

KE–momentum relation

Momentum from KE

Work–energy theorem

Potential energy

Conservative force from PE

Gravitational PE

Elastic (spring) PE

Conservation of mechanical energy

Change in PE

Average power

Instantaneous power

Work by gravity

Work by a spring

Work by friction

Stable equilibrium

Unstable equilibrium

Neutral equilibrium

Conservative force (curl)

Horsepower

Work as area

KE is non-negative

Modified work–energy theorem

Power–velocity (constant P)

Efficiency

Work done in a round trip (conservative)

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