Question

If a car starts from rest and accelerates uniformly , the distance it travels is is proportional to to the ________ of the time it travels

Answer 1

Solution :

✴ Given :-

▪ A car starts from rest and accelerates uniformly.

✴ To Find :-

▪ Distance covered by body is proportional to the ___ of the time interval.

✴ Formula :-

▪ As per third equation of kinematics, Formula of distance covered by body in uniform acceleratory motion is given by...

$\boxed{\sf{\pink{\large{s = ut + \dfrac{1}{2}at^2}}}}$

✴ Terms indication :-

• s denotes distance traveled by body
• u denotes initial speed
• a denotes acceleration
• t denotes time interval

✴ Calculation :-

$\implies\sf\:s=(0\times t)+ \dfrac{1}{2}at^2\\ \\ \implies\sf\:s=\dfrac{1} {2}at^2\\ \\ \red{\sf\dag\:here\:acceleration\:is\:constant}\\ \\ \therefore\:\boxed{\tt{\orange{\large{s\propto t^2}}}}$

_________________________________

✒ Distance travels by body is proportional to the $\bf{t^2}$ of the time it travels.

Answer 2

GiveN :

• Car starts from rest.
• Acceleration is uniform

To FinD :

If a car starts from rest and accelerates uniformly , the distance it travels is is proportional to the ________ of the time it travels.

SolutioN :

Use 2nd equation of motion :

$\dashrightarrow \boxed{\tt{S \: = \: ut \: + \: \dfrac{1}{2} at^2}} \\ \\ \dashrightarrow \tt{S \: = \: 0 \: \times \: t \: + \: \dfrac{1}{2} at^2} \\ \\ \dashrightarrow \tt{S \: = \: 0 \: + \: \dfrac{1}{2} at^2} \\ \\ \dashrightarrow \tt{S \: = \: \dfrac{1}{2} at^2} \\ \\ \dashrightarrow \tt{S \: \propto \: t^2} \\ \\ \sf{Where \: \dfrac{a}{2} \: is \: constant}$

If a car starts from rest and accelerates uniformly , the distance it travels is directly proportional to the square of the time it travels