Question

A man is driving a car with a speed of 80 km/h . suddenly he saw a child walking midway on road which is at 200 m from car, calculate the retardation of car to avoid accident and

also draw the velocity time graph for the motion of car.​

Answer 1

$\LARGE{\bf{\underline{\underline{GIVEN:-}}}}$

• Initial velocity (u) = 80 kmhr⁻¹ ⇒ 200/9 ms⁻¹.
• Final velocity (v) = 0ms⁻¹ [Because the car has to stop in order to avoid accident]
• Distance (d) = 200 m.

$\LARGE{\bf{\underline{\underline{TO:FIND:-}}}}$

• We need to calculate the retardation of the car so that no accident takes place.

$\LARGE{\bf{\underline{\underline{SOLUTION:-}}}}$

▣ We can calculate retardation using this formula:

$\to \sf{\red{2as =v^2-u^2 }}$

Where:

• a is acceleration\retardation.
• s is distance.
• v is final velocity.
• u is initial velocity.

▣ Substituting the values, we get:

$\to \sf 2 \times a \times 200 =0^2- \left(\dfrac{200}{9} \right)^2$

$\sf \to a \times 400 =- \left(\dfrac{40000}{81} \right)$

$\sf \to a =- \left(\dfrac{40000}{81 \times 400} \right)$

$\sf \to a=-\dfrac{100}{81}$

$\leadsto \boxed{\sf{\green{a=-1.23ms^{-2} }}}$

Velocity-time graph is given below:

(I used wolfram to plot the graph)

NOTE: The values are approximate.

Some kinematic equations:

$\boxed{\substack{\displaystyle \sf v=u+at \\\\ \displaystyle \sf s=ut+\dfrac{1}{2}gt^2 \\\\ \displaystyle \sf 2as=v^2-u^2}}$