2.12 Solving Problems for Motion Under Gravity

2.12 Solving Problems for Motion Under Gravity

Three equations of motion are used to solve problems for the motion of bodies. If v_i is the initial velocity of the body, v_f is the final velocity, t is the time taken, S is the distance covered, and a is the acceleration, then:

v_f = v_i + at              ............ (1)
S = v_i t + 1/2 at²         ............ (2)
2aS = v_f² − v_i²           ............ (3)

While applying these equations, the following assumptions are made:

1. Motion is always considered along a straight line.
2. Only the magnitudes of vector quantities are used.
3. Acceleration is assumed to be uniform.
4. The direction of initial velocity is taken as positive. Other quantities which are in the direction of initial velocity are taken as positive. The quantities in the direction opposite to the initial velocity are taken as negative.