Question

Derive velocity-time relation and position-time

relation for a uniformly accelerated motion by

graphical method.​

Answer 1

we have to derive velocity-time relation and position-time relation for a uniformly accelerated motion by graphical method.

(1) velocity - time relation.

let a particle is moving with velocity u after time t its velocity becomes v. due to uniform acceleration a.

see graph,

slope of velocity - time graph = acceleration of particle

⇒(v - u)/(t - 0) = a

⇒v - u = at

⇒v = u + at , this is required relation of velocity-time in uniformly accelerated motion.

(2) position- time relation.

area under position time graph = displacement covered by particle during time t,

see figure,

⇒displacement covered by particle, s = area of trapezium

= 1/2 (u + v) × t

now using v = u + at

⇒s = 1/2 (u + u + at) × t

⇒s = 1/2 (2u + at) × t

⇒ s = ut + 1/2 at² this is required relation of position- time in uniformly accelerated motion.

Answer 2

Answer:

the correct option is b v = u+at

Explanation:

it may help u lot