Intro to Acceleration Practice Problems

During a festival, a hot air balloon which is initially at rest was released and moved upward from the ground. During the first 70.0 s of its motion, its vertical acceleration is defined by ay = (0.008 m/s³)t. Follow the convention that upward motion is positive. Determine the speed of the hot air balloon when it has reached a height of 6 m.

During a festival, a hot air balloon which is initially at rest was released and moved upward from the ground. During the first 70.0 s of its motion, its vertical acceleration is defined by ay = (0.008 m/s³)t. Follow the convention that upward motion is positive. Determine the height of the hot air balloon at t = 70.0 s.

A train is traveling to the right along its straight railway track. The equation for the position of the train as a function of time is given by x(t) = 25.0 cm + (3.15 cm/s)t − (0.0324 cm/s²)t². What are the initial position, initial velocity, and initial acceleration of the train?

The velocity of a squirrel running around the forest is defined by v_x(t) = α + βt², where α = 4.50 m/s and β = 0.270 m/s³. Considering t = 0 to t = 12.00 s, what is the squirrel's average acceleration?

The westward component of the velocity of a truck that travels from rest and along Rama Street is given by v_x(t) = ( − 2.134 m/s³)t². What is the acceleration of the truck when v_x = − 17 m/s?

An airplane stands still on the runway to take off. The plane starts from zero initial velocity, heads in a straight path, and achieves a speed of 100 m/s (360 km/h) before taking off. If the plane covered a distance of 1800 m, what is the time taken by the plane to travel this length of the runway?

A train is stopped at a red light. As soon as the light turns green, the train starts with constant acceleration along the rails. The train starts with zero initial velocity, going into the straight path, and moves with the speed of 22.22 m/s when it reaches the next light at a distance of 130 m from the previous one. What is the magnitude of the acceleration of the train?

A horse is trotting on a road whose position (in meters) is given as a function of time (in sec) as x = At⁵ + Bt³. Determine the expression for its acceleration as a multiple of t.

A school bus is heading to school at a constant velocity. After covering a distance of 140 m in 5.0 s, the driver applies brakes on a traffic signal and comes to rest in 4.0 s. Determine the magnitude of its acceleration in i) m/s² and ii) in terms of the gravitational constant (g).

The equation a_x = 7•v_x + 4 gives the acceleration of a body starting from rest. Determine an equation for the velocity of the body as a function of time.

The velocity of a moving body is modeled by the equation v_x = (t² - 5t + 6) m/s, where t is in seconds. Determine the acceleration of the body at the points where the body reverses its direction.

The motion diagram (velocity vector) in the given figure represents an object that is slowing down and bending downward. What should be the direction of its acceleration vector?

A block suspended freely exhibits a velocity given by the equation v_x = (3.5 m/s)cos(π•t), where t denotes time in seconds. Determine the acceleration of the block when it first reverses its direction.