A truck accelerates from speed upsilon to 2 upsilon. Work done in during this is

Question

A truck accelerates from speed upsilon to 2 upsilon. Work done in during this is (A) three times as the work done in accelerating it from rest to upsilon (B) same as the work done in accelerating it from rest to upsilon (C) four times as the work done in accelerating it from rest to upsilon (D) less than the work done in accelerating it from rest to upsilon

Tardigrade Admin · Accepted Answer

Work done to accelerate from 0 to v is, W1=(1/2) m v2 Work done to accelerate from v to 2 v is W2 =(1/2) m (2 v)2 ⇒ Δ W =W2-W1=(1/2) m(2 v)2-(1/2) m v2 =4 W1-W1=3 W1

Q. A truck accelerates from speed $υ t o 2 υ$ . Work done in during this is

three times as the work done in accelerating it from rest to $υ$

same as the work done in accelerating it from rest to $υ$

four times as the work done in accelerating it from rest to $υ$

less than the work done in accelerating it from rest to $υ$

Work done to accelerate from $0$ to $v$ is, $W_{1} = \frac{1}{2} m v^{2}$
Work done to accelerate from $v$ to $2 v$ is
$W_{2} = \frac{1}{2} m (2 v)^{2}$
$\Rightarrow Δ W = W_{2} - W_{1} = \frac{1}{2} m (2 v)^{2} - \frac{1}{2} m v^{2}$
$= 4 W_{1} - W_{1} = 3 W_{1}$

Q. A truck accelerates from speed υto2υ. Work done in during this is

three times as the work done in accelerating it from rest to υ

same as the work done in accelerating it from rest to υ

four times as the work done in accelerating it from rest to υ

less than the work done in accelerating it from rest to υ