Representing Motion

A car accelerates from rest with a constant acceleration of 3.0 m/s². What distance does the car cover during the first 6.0 s of motion?

An object starts from rest and undergoes constant acceleration. The distance it covers in the first 2.0 s is d. What distance does it cover in the first 4.0 s?

A velocity–time graph shows a straight line that begins at vₓ = 10 m/s at t = 0 and reaches vₓ = 30 m/s at t = 4.0 s. What is the displacement of the object during this interval?

A ball is thrown vertically upward at 30 m/s from the ground. Using g ≈ 10 m/s², what is the total time the ball spends in the air before returning to its launch height?

A stone is dropped from rest off a bridge and strikes the water 2.0 s later. Using g ≈ 10 m/s², what is the height of the bridge above the water?

The position of a particle is given by x(t) = 5t³ − 2t (in metres). What is the instantaneous acceleration of the particle at t = 1.0 s?

A train traveling at 40 m/s applies its brakes and decelerates uniformly at 2.0 m/s². How far does the train travel before coming to a complete stop?

An object’s velocity is given by vₓ(t) = 6t² + 4 (in m/s). What is the displacement of the object from t = 0 to t = 2.0 s?

A delivery drone descends vertically, and its velocity–time graph shows a straight line from vᵧ = −12 m/s at t = 0 to vᵧ = −4.0 m/s at t = 4.0 s (taking downward as negative). Which statement correctly describes the drone’s motion during this interval?

A rocket-powered sled starts from rest. During the first 5.0 s, its acceleration is 4.0 m/s². During the next 5.0 s, its acceleration increases to 8.0 m/s². What is the sled’s velocity at t = 10 s?

A child on a water slide starts from rest at the top and reaches 8.0 m/s at the bottom, traveling a distance of 16 m along the slide. Assuming constant acceleration along the slide, what is the magnitude of the acceleration?

An object moves along a straight line. Its position–time graph is a downward-opening parabola with its vertex at t = 3.0 s. Which description of the object’s motion at t = 3.0 s is correct?

Two students drop balls from the same height at the same instant. Student A’s ball has a mass of 0.5 kg and Student B’s ball has a mass of 2.0 kg. Neglecting air resistance, how does the speed of ball A compare to the speed of ball B just before hitting the ground?

An engineer is testing a braking system. At 20 m/s the car stops in 40 m. The engineer then tests at 40 m/s with the same braking deceleration. What stopping distance should the engineer expect?

The velocity of a particle is vₓ(t) = 8 − 2t (in m/s). At what time does the particle change direction, and what is its displacement from t = 0 to t = 6.0 s?

A ball is launched straight upward from the roof of a 45 m tall building at 20 m/s. Using g ≈ 10 m/s², what is the ball’s velocity just before it strikes the ground at the base of the building?

An object’s acceleration is given by aₓ(t) = 12t (in m/s²) and it starts from rest at the origin. What is the object’s position at t = 2.0 s?

A cyclist travels at a constant velocity of 10 m/s for 4.0 s, then accelerates uniformly at 2.0 m/s² for the next 6.0 s. What is the total displacement over the entire 10 s?

A student plots a velocity–time graph for a moving object. Between t = 2.0 s and t = 5.0 s, the curve is above the time axis but has a negative slope. Which statement best describes the object’s motion during this interval?

A physics teacher drops a ball from a second-floor window. A student standing on the ground starts a stopwatch when the ball is released and records that it takes 1.4 s to reach the ground. The student then calculates the window height. Another student claims the ball must have been thrown downward because “things don’t fall that fast from only one storey.” Using g ≈ 10 m/s², determine the height of the window and evaluate the second student’s claim.