Apex class • iitJEE Kinematics Lab
Position (x-t), Velocity (v-t) & Acceleration (a-t) Synchronizer
Switch motion types and tap the Time Checkpoints below to see how Slopes & Areas connect all 3 graphs!
1. Position-Time (x-t)
x = t² (Smile ∪)
📐 Slope (dx/dt) = Velocity: Curve gets steeper every second because velocity is increasing!
2. Velocity-Time (v-t)
v = 2t (Linear)
🔺 Slope = +2 m/s² (Constant) | Shaded Area = Displacement (x)!
3. Accel-Time (a-t)
a = +2 m/s² (Flat)
🟩 Rectangle Area (a × t) = Change in Velocity (Δv)!
Position (x = t²)
0.0 m (At Origin)
4.0 m
16.0 m (4× Distance!)
Velocity (v = dx/dt = 2t)
0.0 m/s (Starts at Rest)
+4.0 m/s
+8.0 m/s
Acceleration (a = dv/dt)
+2.0 m/s² (Constant)
1. Position-Time (x-t)
x = 8t – t² (Frown ∩)
⛰️ Braking Curve: Slope flattens out until v = 0 at t = 4s (Maximum Stopping Distance = 16m)!
2. Velocity-Time (v-t)
v = 8 – 2t (Falling)
📉 Negative Slope (-2 m/s²): Velocity drops steadily to 0 at t = 4s.
3. Accel-Time (a-t)
a = -2 m/s² (Below 0)
🛑 Negative Area below Time Axis: Subtracts from initial speed!
Stopping Position (x = 8t – t²)
0.0 m (Brakes Applied)
12.0 m
16.0 m (Stopped at Peak!)
Velocity (v = 8 – 2t)
+8.0 m/s (Fast)
+4.0 m/s (Slowing)
0.0 m/s (Rest!)
Retardation (a = dv/dt)
-2.0 m/s² (Braking)
1. Position-Time (x-t)
x = 4t (Straight Line)
📏 Constant Slope: Covers equal distance (8m) in every 2-second interval!
2. Velocity-Time (v-t)
v = 4 m/s (Flat)
🟨 Zero Slope (dv/dt = 0): Speed stays locked at 4 m/s!
3. Accel-Time (a-t)
a = 0 m/s² (Zero)
⚖️ Zero Acceleration: Net force is zero (Newton’s 1st Law)!
Position (x = 4t)
0.0 m
8.0 m
16.0 m
Velocity (v = Constant)
+4.0 m/s (Unchanged)
Acceleration (a = 0)
0.0 m/s²
📐 Moving Right (Take Slope):
Slope of x-t = v | Slope of v-t = a
Slope of x-t = v | Slope of v-t = a
🟧 Moving Left (Take Area):
Area of a-t = Δv | Area of v-t = Δx
Area of a-t = Δv | Area of v-t = Δx
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