The speed of an object moving through a viscous fluid is given by v(t)=A⋅e^(−b⋅t). (a) If the numerical value of A (in SI units) is 3.20 and the numerical value of b (in SI units) is 1.31, then what is the initial acceleration of the particle, at time t=0? (b) How far does the particle move in the first 2.00s? You may ignore gravity. The particle has the same density as the fluid.

Please answer the first three parts (a, b, c)

An object is travelling in 1-dimension (i.e. along the x- axis) with a velocity described by the equation: v(t)=v0+1/6st^3 , where s and v0 are constants. The object’s position, and acceleration at time t = 0 are given by d0, and a0 respectively. In terms of the variables given, what is the average acceleration of the object over the interval from 0 to 2 seconds.

Nerve impulses in a human body travel at a speed of about 100 m/s. Suppose a woman accidentally steps barefoot on a thumbtack. About how much time does it take the nerve impulse to travel from the foot to the brain (in s)? Assume the woman is 1.80 m tall and the nerve impulse travels at uniform speed.

A particle moves so that its position (in meters) as a function of time (in seconds) is r = î + 5t2 j + 5t k. (Use the following as necessary: t.) (a) Write an expression for its velocity as a function of time. V = m/s (b) Write an expression for its acceleration as a function of time. a = m/s?

An object's position as a function of time in one dimension is given by the expression; 3.89t2 + 2.22t + 7.48 where are constants have proper SI Units. What is the object's average velocity between the times t = 3.16 s and t = 8.38 s? with everything in 3 sig figs

A jeep travels a distance d=22.1m in the positive x direction in a time t1=20.2s, at which point the jeep brakes, coming to rest in t2=7.38s. 1. What was the jeep's instantaneous velocity in the horizontal direction, in meters per second, when it began braking?  2. Using the result from question 1, what was the jeep's horizontal component of acceleration, in meters per squared second, during the braking period?

A proton moves along the x axis according to the equation x = 54 t+ 11 t2, where x is in meters and t is in seconds. Calculate (a) the average velocity of the proton during the first 3.0 s of its motion, (b) the instantaneous velocity of the proton at t = 3.0 s, and (c) the instantaneous acceleration of the proton at t = 3.0 s. (a) Number i Units (b) Number i Units (c) Number i Units

I don't understand how to do this problem. I tried taking the derivative, but that didn't give me the correct answer. I would really appreciate the help. When a 1984 Alpha Romeo Spider sports car accelerates in the x-direction at the maximum possible rate,its motion during the first 20. seconds is extremely well modeled by the simple equation vx2=(60 m2/s3)t, where t is time in seconds and vx is in m/s. In other words, the squareof teh car's velocity increases linearly with time. What is its acceleration after 3s, assuming that the car starts from rest at t=0 s?