The motion of a particle along a straight line is described by equation : x = 8 + 12 t - t3 Where x is in metre and t in second. The retardation of the particle when its velocity becomes zero, is:

  • Option 1)

    24 ms-2

  • Option 2)

    Zero

  • Option 3)

    6 ms-2

  • Option 4)

    12 ms-2

 

Answers (1)

As we learnt in

Introduction to Differentiation -

frac{d}{dx}left ( x^{n} 
ight )={n} x^{n-1}
 

- wherein

frac{d}{dx}left ( x^{5} 
ight )=left ( n=5 
ight )

Rightarrow {n}x^{n-1}

Rightarrow {5}x^{5-1}

Rightarrow {5}x^{4}

 

 

 

x=8+12t-t^{3}

v=\frac{dx}{dt}=12-3t^{2}

Put v=0            3t^{2}=12,            t=2 \sec

a=-6 \times 2=-12m/s^{2}

Retardation = 12m/s^{2}

Correct option is 4.


Option 1)

24 ms-2

Incorrect

Option 2)

Zero

Incorrect

Option 3)

6 ms-2

Incorrect

Option 4)

12 ms-2

Correct

Most Viewed Questions

Preparation Products

JEE Foundation + Knockout JEE Main 2025 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
JEE Foundation + Knockout JEE Main 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
Knockout JEE Main 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Knockout BITSAT 2021

It is an exhaustive preparation module made exclusively for cracking BITSAT..

₹ 4999/- ₹ 2999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions