Motion

Distance can never be zero if the body has moved; displacement can be zero even if the body has moved

Step 1: Distance is the total path length traveled, regardless of direction. It is a scalar quantity and always positive or zero. Step 2: Displacement is the shortest straight-line distance from the initial to the final position, and it is a vector quantity. Step 3: If a person walks in a circle and returns to the starting point, the distance traveled equals the circumference of the circle (non-zero), but displacement = 0 because initial and final positions are the same. Step 4: Distance can never decrease or be zero (unless no movement), while displacement CAN be zero after movement. Step 5:

Slope of the velocity-time graph

Step 1: Acceleration is defined as the rate of change of velocity, i.e., a = Δv/Δt = (v-u)/t. Step 2: On a velocity-time graph, the Y-axis is velocity and the X-axis is time. The slope of any graph = change in Y / change in X. Step 3: Therefore, slope of v-t graph = Δv/Δt = acceleration. For uniform acceleration, this slope is constant and gives a straight line. Step 4: The area under the v-t graph gives displacement (not acceleration). Step 5: The slope of the distance-time graph gives speed. The ratio of total displacement to total time gives average velocity. These are commonly confused qua

50 m

Step 1: The car starts from rest (u=0). In the first second, s = ½at² → 10 = ½×a×1² → a = 20 ms⁻². Step 2: Distance covered in 3 seconds total: s₃ = ½×20×9 = 90 m. Step 3: Distance covered in 2 seconds total: s₂ = ½×20×4 = 40 m. Step 4: Distance covered in the 3rd second ALONE = s₃ - s₂ = 90 - 40 = 50 m. Step 5: A key concept is that for uniform acceleration from rest, distances covered in successive seconds are in the ratio 1:3:5:7... (odd numbers). First second = 10 m, second second = 30 m, third second = 50 m – confirming our answer. Wrong options arise from confusing cumulative distance wi

4 ms⁻¹

Step 1: For uniform circular motion, speed v = 2πr/T, where r is the radius and T is the time period for one revolution. Step 2: Given: r = 7 m, T = 11 s, π = 22/7. Step 3: v = 2 × (22/7) × 7 / 11 = 2 × 22 / 11 = 44/11 = 4 ms⁻¹. Step 4: Note that even though the speed is constant (uniform circular motion), the velocity direction keeps changing at every point, so this is still an accelerated motion. Step 5: Common mistake – students forget to multiply by 2 in 2πr (full circumference = 2πr, NOT πr). πr is only half the circumference. Option 2 ms⁻¹ results from using πr instead of 2πr.