Please help me with this problem

and Instantaneous Acceleration) 1. (70 pts total) A particle moves so that its position (in meters) as a function of time (in seconds) is: F = (4.00t2)8 + (1.00t4 - 3.00t3 + 5.00)/ + (1.00t4 - 3.00t3 + 5.00)k The units of the coefficients of the position vector are not shown. You do not need to carry units in you calculations for this problem, but make sure to include units in the final answers of problems c - g Report all answers to the correct number of significant figures. a. (10 pts) Using calculus, derive an expression for the velocity is as a function of time t in unit vector notation. b. (10 pts) Using calculus, derive an expression for the acceleration a as a function of time t in unit vector notation. c. (10 pts) Using your answer to la, calculate i at t = 0.500 s in unit vector notation. d. (10 pts) Using your answer to la, calculate i at t = 1.50 s in unit vector notation. e. (10 pts) Using your answer to 1c, calculate the magnitude v of v at t = 0.500 s. f. (10 pts) Using your answer to 1d, calculate the magnitude v of v att = 1.50 s. g. (10 pts) Making use of the appropriate previous answers from above, calculate the average acceleration dave of the object for the time interval from t = 0.500 s to t = 1.50 s in unit vector notation