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- (8) A particle is thrown vertically upwards in the air. The distance it covers in time t is given by =(1) = ut -gr where u is the initial velocity and g denotes the acceleration due to gravity. The velocity of the particle at time tis . u-gt b) at gt d) gt^2Q3) Find the derivatives of the following functions a) If y=cos u, u=2x+/2 find dy/dx at point(0,2) b) Find for the function y =+ v c) if x? + cos-xy + In(y) + 2* =1 then find y' drA particle moves along a line so that its velocity at time t is v() = – † + t + 6 (measured in meters per second). a. Find the displacement of the particle during the time period 1sts4. b. Find the distance traveled during this time period.
- Find the solution of the wave equation when initial velocity equal to O and initial deflection is (2kx/l) when x between zero and (1/2) and deflection equal to (2k(l- x)/I) when x between (1/2) and (1) the P.D.E. is * dt? dx²6. An ant crawls along a linear path with a velocity of v(t) = cos(3t) inches per minute. (a) What is the ant's displacement on the time interval [0, 7/2]? Include units. (b) How far did the ant travel on the time interval [0, 7/2]? Include units.