Displacement Velocity And Acceleration

A remote-controlled car starts at position x₀ = 7 m on a straight track. It drives in the negative direction and stops at position x = −9 m. What is the displacement of the car?

A jogger runs 200 m north, then turns around and runs 120 m south. The entire trip takes 80 s. Calculate the average velocity of the jogger.

A delivery drone accelerates from rest to 18 m/s east in 6.0 s, then maintains that velocity for another 10.0 s. Determine the average acceleration over the entire 16.0 s interval.

The position of a particle is given by x(t) = 3t³ − 5t + 2 (SI units). What is the instantaneous acceleration of the particle at t = 2 s?

A particle has an acceleration given by a(t) = 8t m/s² and an initial velocity v(0) = −4 m/s. At what time does the particle momentarily come to rest?

An ice skater glides in a perfect circle at a constant speed of 5.0 m/s. Which statement correctly describes the skater’s acceleration?

A research balloon rises vertically from position x₀ = 0 m to x = 500 m, then descends to x = 200 m. The total trip takes 100 s. Which pair of values correctly gives the displacement and the average velocity?

The position of an object is described by x(t) = 2t² + 3 (SI units). What is the object’s instantaneous velocity at t = 0 s?

A spacecraft has velocity v(t) = 12t² + 5 m/s and starts at x(0) = 0. What is the position of the spacecraft at t = 3 s?

A train travels at 30 m/s west for 200 s, then at 10 m/s west for 100 s. Calculate the average velocity for the entire journey.

At a certain instant, a car has a positive velocity and a negative acceleration. Which description of the car’s motion at that instant is correct?

For the position function x(t) = t³ (SI units), a student claims that the instantaneous velocity at t = 2 s equals the average velocity over the interval from t = 0 to t = 4 s. Is this claim correct?

An engineer tests a sensor by programming a robot arm to move according to x(t) = −t² + 6t (SI units). At what time does the arm reverse direction?

A particle has acceleration a(t) = 12t (SI units), initial velocity v(0) = 0, and initial position x(0) = 5 m. Determine the position of the particle at t = 2 s.

On a velocity-time graph, a car’s motion is represented by a straight line that starts at v = 20 m/s at t = 0 and decreases to v = 0 at t = 10 s. What does the area under this line segment represent, and what is its value?

A marble rolls along a track described by x(t) = t⁴ − 4t (SI units). At what time is the marble’s velocity equal to zero?

Two cyclists start at the same point. Cyclist A rides 10 km east, while Cyclist B rides 6 km east, then 8 km north. Which cyclist has the greater magnitude of displacement?

A particle’s position is given by x(t) = 6t² − t³ (SI units). Determine the time at which the particle’s acceleration is zero.