Representing Motion
A motion diagram shows an object moving to the right with dots that are evenly spaced. Which statement correctly describes the object’s motion?
A ball is rolled to the right on a surface and gradually slows to a stop. Which combination of velocity and acceleration arrow directions is correct for a motion diagram of this ball?
A rocket sled starts from rest and accelerates at a constant 4.0 m/s² for 10.0 s. What is the displacement of the sled during this interval?
An engineer needs to determine how far a braking car travels but does not know the braking time. The engineer knows the initial speed, final speed, and acceleration. Which kinematic equation is most appropriate?
A truck traveling at 30 m/s brakes with a constant deceleration of magnitude 6.0 m/s². Calculate the stopping distance.
A stone is dropped from rest off a bridge 80 m above a river. How long does the stone take to reach the water? (Use g = 10 m/s².)
A ball is thrown vertically upward at 30 m/s. What is the maximum height reached by the ball? (Use g = 10 m/s².)
At the very top of its trajectory, a ball thrown straight up has a velocity of zero. What is the acceleration of the ball at this instant?
A spacecraft on a distant planet drops a probe from rest and records that the probe falls 50 m in 5.0 s. A scientist claims the gravitational acceleration on this planet is 10 m/s². Is this claim correct?
An object starts from rest and undergoes constant acceleration. If it travels 20 m in the first 4.0 s, how far does it travel in the first 8.0 s?
A velocity–time graph shows a straight line starting at v = 6.0 m/s at t = 0 and reaching v = 18 m/s at t = 6.0 s. What is the acceleration and displacement during this interval?
On a position–time graph, an object’s trajectory is a downward-opening parabola. Which description of the object’s motion is correct?
A velocity–time graph for an object shows velocity starting at +8.0 m/s, crossing zero at t = 4.0 s, and reaching −8.0 m/s at t = 8.0 s. What is the displacement of the object from t = 0 to t = 8.0 s?
A car accelerates from rest at 3.0 m/s² for 6.0 s, then travels at constant velocity for another 10.0 s. What is the total displacement over the entire 16.0 s?
A student states: “A negative acceleration always means the object is slowing down.” Which scenario correctly disproves this claim?
Two identical balls are dropped from rest, one from a height of 20 m and another from a height of 80 m. What is the ratio of the time for the higher drop to the time for the lower drop?
A research team launches a sensor package straight up from ground level at 40 m/s. They need it to reach a weather balloon hovering at exactly 60 m above the ground. An intern says, “It will reach 80 m, so it will definitely pass the balloon.” Determine whether the sensor package reaches the balloon, and calculate the speed of the package at 60 m height.
The area under an acceleration–time graph between t = 2.0 s and t = 6.0 s is 12 m/s. If the object’s velocity at t = 2.0 s is 5.0 m/s, what is the velocity at t = 6.0 s?
A toy car moves along a track. Its position–time graph is a straight line with a positive slope for the first 5 seconds, then a horizontal line for the next 5 seconds, and finally a straight line with a negative slope (steeper than the first segment) for the last 3 seconds. Which velocity–time graph correctly represents this motion?
A ball is launched vertically upward from the edge of a 60 m tall building with an initial speed of 20 m/s. Determine the total time for the ball to reach the ground below. (Use g = 10 m/s².)