Prove the equation s = u t + 1 2 a t 2 .

Consider the linear motion of a body with an initial velocity u . Let the body accelerate uniformly and acquire a final velocity v after time t . The velocity–time graph is a straight line A B as shown below. At t = 0 , initial velocity = u = O A At t = t , final velocity = v = O C The distance S travelled in time t = area of the trapezium O A B D s = 1 2 × ( O A + D B ) × O D s = 1 2 × ( u + v ) × t Now, from first equation of motion, v = u + a t s = 1 2 × ( u + u + a t ) × t s = t 2 ( 2 u + a t ) s = u t + 1 2 a t 2 Hence, proved.

E M B I B E

A Text Book of PHYSICS PART I : CLASS 11>Chapter 5 - Motion of a Particle>EXERCISE>Q 7

MEDIUM

11th West Bengal Board

IMPORTANT

Earn 100

What is the role of centripetal acceleration on the circular motion ?

Important Questions on Motion of a Particle

EASY

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 5 - Motion of a Particle>EXERCISE>Q 1

Define acceleration. Establish the equation

v = u + a t

.

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 5 - Motion of a Particle>EXERCISE>Q 2

Prove the equation

s = u t + \frac{1}{2} a t^{2}

.

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 5 - Motion of a Particle>EXERCISE>Q 3

Show that the instantaneous acceleration at any point in the velocity-time graph equals the slope of the tangent to the graph at that point. Which one is more important in the laws of mechanics - the average acceleration or the instantaneous acceleration ?

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 5 - Motion of a Particle>EXERCISE>Q 4

Prove the equation :