Question

the average frictional force needed to stop a car
ating 500 kg in a distance of 25 m if the initial speed​

Answer 1

Question:-

Find the average frictional force needed to stop a car weighing 500 kg in a distance of 25 m if the initial speed is 72 km/h.

Answer:-

$\displaystyle\large\boxed {\sf {F=-4\ kN}}$

Solution:-

Given,

★ mass of the car, $\displaystyle\sf {m=500\ kg.}$

★ stopping distance travelled by the impact of frictional force, $\displaystyle\sf {s=25\ m.}$

★ initial speed, $\displaystyle\sf {u=72\ km\ h^{-1}=20\ m\ s^{-1}}$

Since the car is brought to rest by the frictional force, the final velocity, $\displaystyle\sf {v=0\ m\ s^{-1}.}$

Then, the retardation acting on the car, by the third kinematic equation, is,

$\displaystyle\longrightarrow\sf {a=\dfrac {v^2-u^2}{2s}}$

$\displaystyle\longrightarrow\sf {a=\dfrac {0^2-20^2}{2\times 25}}$

$\displaystyle\longrightarrow\sf {a=\dfrac {0-400}{50}}$

$\displaystyle\longrightarrow\sf {a=-8\ m\ s^{-2}}$

Then the average frictional force required is,

$\displaystyle\longrightarrow\sf {F=ma}$

$\displaystyle\longrightarrow\sf {F=500\times-8}$

$\displaystyle\longrightarrow\sf {\underline {\underline {F=-4000\ N}}}$

Or,

$\displaystyle\longrightarrow\sf {\underline {\underline {F=-4\ kN}}}$

The negative sign shows nothing but that the frictional force is acting opposite to the displacement.