Question

A truck accelerates from speed $v$ to $2v$. Work done is during this is

• A. Three times as the work done in accelerating it from rest to $v$
• B. Same as the work done in accelerating it from rest to $v$
• C. Four times as the work done in accelerating it from rest to $v$
• D. Less than the work done in accelerating it from rest to $v$

Answer 1

The correct option is A Three times as the work done in accelerating it from rest to $v$

Work done $W=\Delta K.E=\frac{1}{2}m(v_2^2-v_1^2)$ ........(1)

Truck accelerates from $v$ to $2v$ :

From (1), $W=\frac{1}{2}m\left(\right(2v{)}^2-v^2)=\frac{3}{2}m{v}^2$

Truck accelerates from rest i.e. $v_1=0$ to $v$ :

From (1), $W_a=\frac{1}{2}m(v^2-0)=\frac{1}{2}m{v}^2$

$⟹$ $W=3W_a$

Hence option A is correct.