Unit 1: Kinematics

The position of a particle is given by x(t) = 3t³ - 2t. What is the acceleration at t = 1 s?

A particle has velocity v(t) = 4t - t² m/s. Find the total displacement from t = 0 to t = 4 s.

The position of a particle is given by [math]. The velocity at t = 2 s is

The velocity of a particle is [math] m/s. The displacement from t = 0 to t = 4 s is

A particle's acceleration is [math] m/s². If [math] m/s and [math], the position at t = 3 s is

The position of a particle is [math]. The maximum speed of the particle is

A particle moves along the x-axis with velocity [math]. The total distance traveled from t = 0 to t = 4 is

A car's position is given by [math]. The velocity at t = 0 is

A particle has velocity [math]. The distance traveled from t = 0 to t = 1 is

A projectile is launched at angle θ above the horizontal with speed [math]. The time of flight is

The position of a particle is [math] m. The speed at t = 1 s is

A particle moves along the x-axis according to [math]. The amplitude of oscillation is

Two vectors [math] and [math]. Their dot product is

A projectile is launched at 30° above the horizontal with an initial speed of 40 m/s. What is the horizontal component of its velocity at the peak of its trajectory? (g = 10 m/s²)

An object is dropped from rest from a height of 80 m. How long does it take to reach the ground? (g = 10 m/s²)

A boat travels at 5 m/s relative to the water. The river flows at 3 m/s. If the boat heads directly across the river, what is the boat's speed relative to the ground?

A car accelerates uniformly from 10 m/s to 30 m/s in 5 seconds. What distance does it cover?

The instantaneous velocity of an object is found by:

For a projectile launched on level ground, the range is maximized at a launch angle of:

The position of a particle is given by x(t) = 3t³ - 6t + 2. What is the acceleration at t = 2 s?

A ball is launched horizontally from a cliff 45 m high. How long until it hits the ground? (g = 10 m/s²)

If the velocity of an object is v(t) = 4t² + 2t, what is the displacement from t = 0 to t = 3?

A particle moves along the x-axis with position [math] (meters). At what time(s) is the particle at rest?

A car accelerates from rest with acceleration [math] m/s². What is the maximum velocity the car reaches?

A projectile is launched from the ground at angle [math] above the horizontal. The horizontal range is maximized when [math] equals 45°. If instead the projectile is launched from a height [math], the angle for maximum range is

A particle has velocity [math] m/s. What is the total distance traveled from [math] to [math] s?

The position of a particle is [math] where [math] and [math] are positive constants. The ratio of the magnitude of acceleration to velocity at any time [math] is

A ball is dropped from rest and falls for 3 s. During which 1-second interval does it travel the greatest distance? (Ignore air resistance)