Kinematics Review – Arjuna JEE (2026) KPP-09

35 question-and-answer flashcards covering core kinematics formulae, graphical interpretations, conceptual statements and key numerical results from the Arjuna JEE (2026) KPP-09 lecture notes.

State the kinematic equation that gives displacement s in terms of initial velocity u, acceleration a and time t.

s = u t + ½ a t²

Which equation relates final velocity v to initial velocity u, acceleration a and displacement s?

v² = u² + 2 a s

Write the kinematic equation that gives final velocity v after time t under constant acceleration a.

v = u + a t

In vertical motion (upward taken positive), what numerical value of g is commonly used in JEE problems?

g ≈ 10 m s⁻² downward (a = –10 m s⁻²)

What is the velocity of a projectile at the highest point of its vertical motion?

Zero

How long does a body thrown vertically upward with speed u take to reach its highest point?

t = u / g

Give the expression for maximum height attained by a body projected vertically upward with speed u.

h_max = u² / (2 g)

Resolve an initial speed u launched at angle θ into horizontal and vertical components.

ux = u cos θ, uy = u sin θ

Write the time-of-flight formula for a projectile that lands back on the same horizontal level.

T = (2 u sin θ) / g

Write the horizontal range formula for a projectile launched from ground level.

R = (u² sin 2θ) / g

What are the SI units of acceleration?

Metre per second squared (m s⁻²)

If a body starts from rest with constant acceleration a, what is its average velocity after time t?

v_avg = ½ a t

When equal distances are covered at speeds v₁ and v₂, what is the average speed?

v_avg = 2 v₁ v₂ / (v₁ + v₂)

When equal times are spent at speeds v₁ and v₂, what is the average speed?

v_avg = (v₁ + v₂) / 2

How do you obtain displacement from a velocity-time graph?

By calculating the area under the v–t curve

What physical quantity is represented by the slope of a velocity-time graph?

Acceleration

What does a zero slope on a displacement-time graph indicate about the particle’s motion?

Its instantaneous velocity is zero (particle at rest at that instant)

On a velocity-time graph, what indicates that the particle has reversed direction?

The velocity crosses zero and changes sign

Define ‘reaction time’ for a driver.

Time interval between noticing the need to brake and actually applying the brakes

If initial speed is doubled while the braking retardation is unchanged, by what factor does the stopping distance change?

It becomes four times larger (distance ∝ v₀²)

What happens to the speed of a particle when its velocity and acceleration have opposite signs?

The particle slows down (speed decreases)

If the speed of a particle is zero throughout a time interval, what must be true about its acceleration during that interval?

Acceleration must also be zero for the entire interval

In the motorcycle problem, what is the maximum forward acceleration the engine can produce?

5 m s⁻²

What is the maximum braking retardation available to the same motorcycle?

10 m s⁻²

A rocket rises with net upward acceleration 10 m s⁻² for 60 s. What maximum height (in km) does it reach?

36 km

After the rocket’s fuel finishes (at 60 s) how long does it continue to rise before momentarily coming to rest?

60 s

A projectile is launched at 60 m s⁻¹, 60° above horizontal. When it is coming down and makes 30° with the horizontal, what is v²?

v² = 1.2 × 10³ m² s⁻² (1200 SI units)

A balloon ascends with 10 m s⁻² for 2 s; then a particle is dropped. Two seconds later, what is the particle’s speed?

0 m s⁻¹ (it momentarily stops)

For the same balloon problem, how high is the particle above the ground after those 4 s?

40 m

State the condition under which the harmonic mean, rather than the arithmetic mean, gives average speed.

When equal distances are covered at two different speeds

What kinematic fact explains why stopping distance quadruples when speed doubles, given constant deceleration?

Because stopping distance s = v₀² / (2 |a|); thus s ∝ v₀²