Question

derive an expression for the distance travelled by a body moving with a uniform motion "a" having initial velocity "u" and final velocity "v" after a time "t" from its velocity - timegraph​

Answer 1

Answer:

Let us 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.

Here, The velocity-time graph is a straight line AB

So, According to the velocity-time graph is

At t=0, initial velocity =u=OA

At t=t, final velocity =v=OC

The distance S traveled in time t = area of the trapezium OABD

s=(

2

1

)×(OA+DB)×OD

s=(

2

1

)×(u+v)×t

Since v=u+at

s=(

2

1

)×(u+u+at)×t

s=ut+(

2

1

)at

2