Suppose that the position of a particle is given by s(t)=3t^3+6t+9 (a) Find the velocity at time t. v(t)= ?   (b) Find the velocity at time t=3 seconds. (c) Find the acceleration at time t. a(t) =  ? m/s^2 (d) Find the acceleration at time t=3 seconds.

An object is moving along a straight path that runs north and south .Its velocity, in feet per minute , is given by  v(t) 18-8t+3t^2, where north is the positive direction. After 10 minutes, is the object north of its starting position or south?

An Object moved in horizontal coordinate line according to f(x) = x^3 - 6x^2 , where f is directed distance from the origin in meters and x is the time in seconds. Find the velocity and the acceleration of the object? When is the object moving to the right? When is the object moving to the left? When is the acceleration negative?

Find f. f ''(t) = 9/square root of t,    f(4) = 26,    f '(4) = 13

A rider is delivering online orders and is traveling along a straight road. The position function of the rider is given by s(t) = (t^3) - (9t^2) + (24t) - 15 where s is measured in kilometers and t is measured in hours. a.) What is the rider’s velocity at the moment when its acceleration is 12 km/(h^2)? b.) At which time interval(s) is the rider slowing down? c.) Find the total distance traveled by the rider in the first three hours

The position of an object in meters at ʼn seconds can be described by the position function s (t) = at³ + bt² + ct+d, where a is -29, b is 4, c is 31, and d is 71. What is the acceleration of the object in m/s² at t = 65 seconds?

You are traveling down a country road at a rate of 95 feet/sec when you see a large cow 300 feet in front of you and directly in your lane. The cow is fearless and staring you down. (Or perhaps she does not understand the gravity of the situation.)Regardless, if you simply hit your brakes, after t seconds, the car will be(t)=95t-9t^2 feet from the point where the brakes were first applied. (i)Must you steer to avoid the cow, or can you rely solely on your brakes? Explain. (ii)Graphj(t), J(t), and''(t) and interpret their meanings in the context .(iii) Is there a time t after which the graphs in part (ii) probably do not accurately model the path of the car? (iv) Write a piece-wise function using j(t) that would more accurately model the path of the car on the interval [0,10], assuming the car did not move after it stopped. Sketch this graph and its derivative.

Convert the equation  f(t)=228e^−0.2t to the form  f(t)=ab^t

+ 8)(6y – 1) = 0 find the second derivative

A ball thrown into the air with height in meters after t minutes is represented by the function f(t)= -49.9t^2+25t+3. a) what is the instantaneous velocity at t=4? b) what is the average acceleration 3 minutes after the ball was thrown? c) what is the instantaneous acceleration at t=3?