An object moves in along the x-axis with an acceleration given by: a = 5t2 + 10t (m/s2). The velocity at t=0.0 s is 3 m/s. Calculate the velocity at t=7 s.

Problem 4: A particle moving along a straight path has an acceleration defined by a = 0.6s + 3.6 ft/s², where s is in feet. If the particle's speed is 1.2 ft/s at s = 0, find its speed when s = 8 feet.

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?

An object moves in along the x-axis with an acceleration given by: a = 9t (m/s2). The position of the object at t=0.0 is 5 m, and its velocity at t=0.0 s is 7 m/s. Calculate the position at t=8 s.

Shown below is a graph of velocity-versus-time for a moving object. The object starts at position x = 0 m at t = 0 s. What is the final position at t = 4.0 s, in meters?

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 skydiver falls d1=355m in t1=8.7s before opening her parachute. After the chute opens, she falls an additional d2=780m in t2=116s. Calculate the skydiver’s average speed, v avg in meters per second, during the entire fall.

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

An airplane has a velocity ofv=(5m/s)i+(4m/s)jatt1=3s. For the time interval from t1=3s to t2=13s the average acceleration is a=(.5m/s2)i+(.2m/s2)j. At 13s find the magnitude and direction of the velocity of the airplane.

Some experimental researcher tells us that the position of an object as a function of time is given by x(t) = at3 - bt2 + ct - d, where the constants are a = 3.6 m/s3, b = 4.0 m/s2, c = 60 m/s and d = 7.0 m. Find the average acceleration over the first 2.4 seconds. A) 18 m/s/s B) 54 m/s/s C)36 m/s/s D) 76 m/s/s