Question

a bullet initially moving with a velocity of 20 m/s strikes a target and comes to rest after penetrating a distance of 0.01m in the target. calculate the retardation produced by the target.

Answer 1

retardation= -ve acc.

Answer 2

Given : -

• Initial velocity of the bullet, u = 20 m/s
• Final velocity of the bullet, v = 0 m/s
• Distance, s = 0.01 m

To find : -

• Retardation produced by the target=?

Solution : -

$\qquad$ ☀️To calculate it we will use the third equation of motion.We know that third equation of motion :-

$\qquad$ ⎘ $\pink{\pmb {\mathfrak{v² - u² = 2as}}}$

Where:-

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• s = Distance

$\qquad\small\underline{\pmb{\sf Substituting \: the\: given\: values \::-}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ (0)² - (20)² = 2(a)(0.01)}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ - (20)² = 2 × a × 0.01}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ - 400 = 2 × a × 0.01}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ - 400 ÷ (2 × 0.01) = a}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ - 20,000 = a}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ a = - 20,000 m/s²}}}$

(Negative acceleration is known as retardation.)

Therefore, the retardation of the bullet is 20,000 m/s²

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$\qquad$☀️Equations of motion :-

$\qquad$ ⑴ v = u + at

$\qquad$ ⑵ s = ut + ½at²

$\qquad$ ⑶ v² - u² = 2as

• v = final velocity
• u = initial velocity
• s = displacement
• t = time taken
• a = acceleration

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