A force F=2t2 is applied to the cart initially at rest. The speed of cart at t=5 s is -

Question

A force F=2t2 is applied to the cart initially at rest. The speed of cart at t=5 s is - <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-ubsaw7aduqzf.png" /> (A) 10ms- 1 (B) 8.33ms- 1 (C) 2ms- 1 (D) zero

Tardigrade Admin · Accepted Answer

F=2t2 ⇒ m(d v/d t)=2t2 ⇒ 10 displaystyle ∫ 0vdv=2 displaystyle ∫ 05t2dt ⇒ 10v=2((t3/3))05 ⇒ v=8.33ms- 1

Q. A force $F = 2 t^{2}$ is applied to the cart initially at rest. The speed of cart at $t = 5 s$ is -

$10 m s^{- 1}$

$8.33 m s^{- 1}$

$2 m s^{- 1}$

zero

$F = 2 t^{2}$
$\Rightarrow m \frac{d v}{d t} = 2 t^{2}$
$\Rightarrow 10 \int_{0}^{v} d v = 2 \int_{0}^{5} t^{2} d t$
$\Rightarrow 10 v = 2 (\frac{t ^{3}}{3})_{0}^{5}$
$\Rightarrow v = 8.33 m s^{- 1}$

Q. A force F=2t2 is applied to the cart initially at rest. The speed of cart at t=5s is -

10ms−1

8.33ms−1

2ms−1