Motion

Speed

Step 1: The slope of any graph is calculated as rise/run or change in y-axis/change in x-axis. Step 2: In a distance-time graph, y-axis represents distance and x-axis represents time. Step 3: Therefore, slope = change in distance/change in time = speed. Step 4: A steeper slope means higher speed, while a gentler slope means lower speed. Step 5: This graphical method helps us visualize and calculate speed easily from motion data.

v = u + at

Step 1: The first equation of motion relates final velocity (v), initial velocity (u), acceleration (a), and time (t). Step 2: It states that final velocity equals initial velocity plus the change in velocity due to acceleration. Step 3: The term 'at' represents the change in velocity over time t with constant acceleration a. Step 4: Other equations relate position and velocity but not specifically velocity-acceleration-time relationship. Step 5: This equation is fundamental for solving problems involving uniformly accelerated motion.

10 m/s

Step 1: Use the first equation of motion: v = u + at. Step 2: Given values: u = 0 (starts from rest), a = 2 m/s², t = 5 s. Step 3: Substitute the values: v = 0 + (2 × 5) = 0 + 10 = 10 m/s. Step 4: The body accelerates uniformly, gaining 2 m/s of velocity every second. Step 5: After 5 seconds, total velocity gained = 2 × 5 = 10 m/s, which matches our calculation.

Uniformly accelerated motion

Step 1: A freely falling object experiences constant gravitational acceleration (g ≈ 9.8 m/s²). Step 2: Since the acceleration is constant, the object's velocity increases by equal amounts in equal time intervals. Step 3: This constant acceleration defines uniformly accelerated motion. Step 4: The object starts from rest (or initial velocity) and continuously gains speed as it falls. Step 5: This is a perfect example of motion with constant acceleration, making calculations predictable using equations of motion.