Uniformly Accelerated Motion E9723B

1. **Problem Statement:** Understand the concept of uniformly accelerated motion, where acceleration $a$ is constant. 2. **Key Formula:** The main equations for uniformly accelerated motion are: $$v = v_0 + at$$ $$s = v_0 t + \frac{1}{2} a t^2$$ $$v^2 = v_0^2 + 2as$$ where: - $v$ is the final velocity, - $v_0$ is the initial velocity, - $a$ is the constant acceleration, - $t$ is the time, - $s$ is the displacement. 3. **Explanation:** - The velocity changes linearly with time due to constant acceleration. - Displacement depends on initial velocity, acceleration, and time. - The third equation relates velocities and displacement without time. 4. **Example:** Suppose a car starts from rest ($v_0=0$) and accelerates at $a=3$ m/s$^2$ for $t=5$ seconds. Calculate the final velocity: $$v = 0 + 3 \times 5 = 15 \text{ m/s}$$ Calculate the displacement: $$s = 0 \times 5 + \frac{1}{2} \times 3 \times 5^2 = \frac{1}{2} \times 3 \times 25 = 37.5 \text{ m}$$ 5. **Summary:** - Use the first formula to find velocity at any time. - Use the second formula to find displacement. - Use the third formula when time is unknown. This covers the basics of uniformly accelerated motion.