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Kinematics Example

Easy DifficultyFE Dynamics

A particle moves in a straight line with constant acceleration. Find its velocity and displacement after a given time.

Kinematics describes motion without regard to forces. For constant acceleration a in one dimension: velocity v = v_{0} + a t and position s = s_{0} + v_{0} t + \frac{1}{2} a t^{2} . Alternatively, v^{2} = v_{0}^{2} + 2 a (s - s_{0}) . v = v_{0} + a t s = s_{0} + v_{0} t + \frac{1}{2} a t^{2} Notation: v_{0} = initial velocity, v = velocity at time t, a = constant acceleration, s_{0} = initial position, s = position at time t .

A particle starts at the origin with initial velocity 5 m/s in the positive direction. It has a constant acceleration of 2 m/s² in the same direction. Find: The velocity of the particle after 4 seconds. The distance traveled (displacement) after 4 seconds.

v_{0} = 5 m/s a = 2 m/s^{2} t = 4 s s_{0} = 0 (origin)

v = v_{0} + a t v = 5 + (2) (4) = 13 m/s

s = s_{0} + v_{0} t + \frac{1}{2} a t^{2} s - s_{0} = 5 (4) + \frac{1}{2} (2) (4)^{2} = 20 + 16 = 36 m

(1) Velocity at t = 4 s : v = 13 m/s . (2) Displacement after 4 s: 36 m (distance from origin).

v = v_{0} + a t, s = s_{0} + v_{0} t + \frac{1}{2} a t^{2}