Task 1 Differentiation a) The equation for s, the distance travelled in metres, in time t in seconds is: s=7+15t+5t2 ds Given that the velocity v = find the equation for v and use it to find the velocity dt when t=A seconds. Give your answer with the correct units. b) The voltage V (in Volts) across a capacitor after time t (in seconds) is given by the equation: V = 10-10e dv What is the value of when t=1 second? dt Give your answer to correct level of engineering accuracy and with the correct units. c) Given that the position p=6sin(507) where p is in metres and t in seconds, find the gradient of the waveform when t = B seconds. Give your answer to the correct level of engineering accuracy and with appropriate units. Integration a) The equation for the velocity v (ms) in time t (sec) is v=20t+12+2 ds Given that v= use integral calculus to find an equation for s given that dt when t=0, s = 6 m Use your equation to find s when = 1 second. b) The force F required to move an object a distance x m is given by: F = 4e2x Given that the equation for work done = [Fdx find an equation for W given that when x=0, W=8 Use this equation to find the value of W when x = C meters.