The velocity of an object as a function of time is given by  v=3t2+5t-12 m/s, where t is in seconds. If the object has a position x = 8.00 m at t = 2.00 s, what is the position of the object at time t = 5.00 s?

Problems 1 through 3, treat the motion of a particle which moves along the s-axis shown in the figure. 0 1 2 3 +s, ft or m 1. The acceleration of a particle is given by a = 2t - 10, where a is in meters per second squared and t is in seconds. Determine the velocity and displacement as functions of time. The initial displacement at t = 0 is so = -4 m, and the initial velocity is vo= 3 m/s. (5 points) 2. The acceleration of a particle is given by a = -ks² where a is in meters per second squared, k is a constant, and s is in meters. Determine the velocity of the particle as a function of its position s. Evaluate your expression for s = 5 m ifk = 0.1 m¹s2 and the initial conditions at time t = 0 are so= 3 m and vo= 10 m/s. (5 points) 3. The acceleration of a particle which is moving along a straight line is given by a = -k√√v, where a is in meters per second squared, k is a constant, and v is the velocity in meters per second. Determine the velocity as a function of both time t and…

A particle moves along the x-axis. Its coordinate in meters is given by x(t) = 12t – 3.0t2, where the time is in seconds. The particle is momentarily at rest at t = O 2.0 s O 3.0 s O 4.0 s 5.0 s

The position of an object as a function of time is given as x = At3 + Bt2 + Ct + D . The constants are A = 2.41 m/s3 B = 1.37 m/s2 ' , C = -4.61 m/s, and D = 3.35 m. What is the velocity of the object at t = 19.10 s? m/s

The position of an object is given as a function of time as x(t) = (-3.00 m/s)t + (1.00 m/s2)t2. What is the average speed of the object between t = 0.00 s and t = 2.50 s?

a particle moves in one dimension, and its position as a function of time is given by x = (1.9m/s)t + (-2.6 m/s^2)t^2  what is the particles average velocity from t = 0.45 s to t = 0.55 s?    what is the particles average velocity from t = 0.49 s to t = 0.51 s?

The function x (t) = -2.1le-1.93t describes the position, in meters, of a particle on the x-axis as a function of time t, in seconds. Find the particle's velocity at time t = 3.05 s.

A juggler throws a bowling pin straight up with an initial speed of 8.2 m/s. How much time elapses until the bowling pin returns to the juggler's hand? 0.84 s 1.68 s O 1.2 s O 2.4 s

This graph shows an object’s velocity versus time as it is moving along the x-axis. Its initial position is x0 = 2.0 m at t0 = 0 seconds. At t = 2.0 seconds, what is the object’s position (in m)?

The velocity of a particle moving along the x-axis varies in time according to the expression v(t) = α - βt2 where α = 52.9m/s , β = 3.72m/s3,  and t is in seconds.  a) Find the acceleration in the time interval from t = 0 to 2.97s in units of m/s2 b) Determine the acceleration of the particle tf = 2.97s in m/s2