Due to an acceleration of 4 m/s² the velocity of a body increases from 10 m/s to 30 m/s in a certain period. Find the displacement (in m) of the body in that period.

CONCEPT:

• Equation of motion: The mathematical equations used to find the final velocity, displacements, time, etc of a moving object without considering force acting on it are called equations of motion.
• These equations are only valid when the acceleration of the body is constant and they move on a straight line.
• There are three equations of motion:

V = u + at

V2 = u2 + 2 a S

\({\text{S}} = {\text{ut}} + \frac{1}{2}{\text{a}}{{\text{t}}^2}\)

Where, V = final velocity, u = initial velocity, s = distance traveled by the body under motion, a = acceleration of body under motion, and t = time taken by the body under motion.

EXPLANATION:

v = 30 m/s, u = 10 m/s, a = 4 m/s²

We know that,

⇒ v² = u² + 2aS

⇒ 2aS = v² – u²

⇒ 2 × 4 × S = 900 - 100

⇒ 8S = 800