Question

draw the distance vs time graph when the speed of a body increases uniformly

Answer 1

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Answer 2

DISTANCE VS TIME GRAPH:

• As per the question, speed of the body increases uniformly.

This means that the body has a constant acceleration.

So, let acceleration be 'a' and body start from rest.

$acc. = a$

$\implies \: \dfrac{dv}{dt} = a$

$\implies \: dv= a \: dt$

$\implies \: \displaystyle \int dv= \int a \: dt$

$\implies \: \displaystyle v = at$

$\implies \: \displaystyle \dfrac{dx}{dt} = at$

$\implies \: \displaystyle dx = at \: dt$

$\implies \: \displaystyle \int dx = a \int t \: dt$

$\implies \: \displaystyle x = \frac{ a{t}^{2} }{2}$

$\implies \: \displaystyle x \propto {t}^{2}$

So, the graph will be parabolic in shape

• Refer to diagram.