An object has a position given by r = [(2.5 m/s^3)t^3 +(3.0 m/s)t]i +[3.0 m -(2.0 m/s^2)t^2]j where all quantities are in SI units. Calculate the magnitude of the acceleration of the object at time t = 2.00 s

The following equations give the position x(t) of a particle in four situations (in each equation, x is in meters, tis in seconds, and t> 0): (1) x = 3t - 4: (2) x = -5t3 + 4t2 + 6: (3) x = 2/t2 - 4/t; (4) x = 5t2 3. (a) In which situation is the acceleration a of the particle constant?

An unidentified flying object (UFO) is observed to travel a total distance of 19000 m, starting and ending at rest, over a duration of 4.23 s. Assuming the UFO accelerated at a constant rate to the midpoint of its journey and then decelerated at a constant rate the rest of the way, what was the magnitude of its acceleration? Express your answer in g s , where 1 g = 9.81 m/s^2.

The coordinates (in meters) of a rabbit’s position as functions of time t (in seconds)are given by:x(t) = −3t2 + 4t − 2y(t) = 6t2 − 4t(a) What are the magnitude and direction of the instantaneous velocities at t = 0and t = 4 seconds?(b) Find the magnitude and direction of the acceleration of the rabbit at t = 1and t = 3 sec.

A car is moving with a velocity (3.0 m/s) + (1.0 m/s) and 2.0 seconds later its velocity is (6.0 m/s) - (3.0 m/s). What is the magnitude of the average acceleration of the car?

An object has a position given by r = [2.0 m + (5.00 m/s)t]i + [3.0 m - (2.00 m/s2)t2]j, wherequantities are in SI units. What is the speed of the object at time t = 2.00 s?

On a spacecraft two engines fire for a time of 567 s. One gives the craft an acceleration in the x direction of ax = 4.80 m/s2, while the other produces an acceleration in the y direction of ay = 7.52 m/s2. At the end of the firing period, the craft has velocity components of vx = 3751 m/s and vy = 4834 m/s. Calculate the magnitude of the initial velocity.

The driver of a car travelling at 65km/h in an easternly direction, steps on the brakes and stops in 4.0s. while braking, the average acceleration of the car in (m/s^2)   A) 16.3 m/s^2 towards the west B) 4.5 m/s^2 towards the west C) 4.5 m/s^2 towards the east D) 16.3 m/s^2 towards the east

The position of an object is given by x = at3 - bt2 + ct,where a = 4.1 m/s3, b = 2.2 m/s2, c = 1.7 m/s, and x and t are in SI units. What is the instantaneous acceleration of the object when t = 3.5 s?

A biologist studying the motion of bacteria notes a bacterium at position r 1=2.2i + 3.7j − 1.2k μm (1μm = 10-6). After 7.2 seconds the bacterium is at r2 = 4.6i + 1.9k μm. Given that the acerage velocity is equal to 0.33i - 0.51j + 0.42k. Calculate the magnitude of the average velocity.