Question

The reader understands derivatives, and knows the definition of instantaneous velocity (dx/dt), and knows how to calculate integrals but is struggling to understand them. Use students’ prior knowledge to provide an explanation that includes the concept and physical meaning of the integral of velocity with respect to time.

Reminder: The user is comfortable with the calculations, but is struggling with the concept. To fully address the prompt, emphasize the written explanation in English over the calculation.

** Take you time. Type the answer and Include a Figure. Do Not Copy Paste Any Answer. **

Answer 1

By definition dx/d+=V X-is X-Co-ordinate of particle at any time t. V-is Velocity of particle at any time +. If vis constant dx=vdt Integratin both side with time we get, t dc = Vat To 0 At time t=0 X=Xi=initial X-co-ordinate. +=+x=Xf -final x co-ordinate. Integrating we get Xf-xi=V+ Xf=Xi+V+ 24 = x+1 So 42 = Displacement in time +=Xf-xi=vt Here v=constant If v=f(t) je v is also function of time we still integrate to find displacement. e.g V=A++B+^2 ㅏ A2 = VCE) dt O lig VE) = 14 +Bt? (A++B+2) dt 4x = (AL? +BE)