Graphs — Position-time, velocity-time, acceleration-time
Kinematics
13
JEE Qs
8%
Hard
75
min
Master the core relationships between position, velocity, and acceleration graphs (slope for derivative, area for integral); this is a foundational skill for kinematics and beyond.
🧮 Key Formulas
✅ Key Points for JEE
- 1The slope of a position-time (x-t) graph at any instant gives the instantaneous velocity. A steeper slope implies a greater magnitude of velocity.
- 2The slope of a velocity-time (v-t) graph at any instant gives the instantaneous acceleration. A positive slope means positive acceleration, negative slope means negative acceleration.
- 3The area under a velocity-time (v-t) graph between two time instants gives the displacement during that interval. Area above the t-axis is positive, below is negative.
- 4The area under an acceleration-time (a-t) graph between two time instants gives the change in velocity during that interval. Always remember to add initial velocity for final velocity.
- 5The curvature (concavity) of the position-time (x-t) graph indicates acceleration: concave up implies positive acceleration, and concave down implies negative acceleration.
⚠️ Common Mistakes
- ✕Confusing 'distance covered' with 'displacement' from a v-t graph: distance requires taking the absolute value of negative area segments, while displacement includes the sign.
- ✕Incorrectly interpreting the sign of velocity or acceleration. A negative slope on a v-t graph indicates negative acceleration, which could mean speeding up in the negative direction or slowing down in the positive direction.
- ✕Assuming constant velocity or acceleration when the graph is not linear in the appropriate context (e.g., a curved x-t graph means non-constant velocity, not necessarily non-constant acceleration).
📝 Practice Questions
See allQ27.A ball having kinetic energy KE, is projected at an angle of 60∘ from the horizontal. What will be the kinetic energy of ball at the highest point of its flight ? (1) (KE) (2) (KE) 8 2 (3) (KE) (4) (KE) 16 4
Q28.The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between t = 0 to t = 4 s ? (1) 30 m (2) 11 m (3) 10 m (4) 13 m
Q50.A particle is projected at an angle of 30∘ from horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is h0 and height traversed in the last second, before it reaches the maximum height, is h1 . The ratio h0 : h1 is _________ [Take, g = 10 m/s2 ]
Q43.The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is _______ km . (1) 12 (2) 3 (3) 6 (4) 9
Q27.The position vector of a moving body at any instant of time is given as →r = . The magnitude (5t2^i −5t^j)m and direction of velocity at t = 2 s is, (1) 5√15 m/s, making an angle of tan−1 4 with - ve (2) 5√15 m/s, making an angle of tan−1 4 with + ve Y axis X axis (3) 5√17 m/s, making an angle of tan−1 4 with + ve (4) 5√17 m/s, making an angle of tan−1 4 with - ve X axis Y axis
Q31.Two projectiles are fired with same initial speed from same point on ground at angles of (45∘−α) and (45∘+ α), respectively, with the horizontal direction. The ratio of their maximum heights attained is : (1) 1−tan α (2) 1−sin 2α 1+tan α 1+sin 2α (3) 1+sin 2α (4) 1+sin α 1−sin 2α 1−sin α
NCERT Chapters
- Class 11 Physics Ch 3: Motion in a Straight Line