A block of mass \(m\) is initially at rest on a frictionless horizontal surface. Starting at time \(t = 0\), a time-varying force \(F(t) = F_0 \sin\left(\dfrac{\pi t}{T}\right)\) is exerted on the block in the positive x-direction for the time interval \(0 \le t \le T\), where \(F_0\) and \(T\) are positive constants. What is the change in velocity of the block during this time interval?