Kinematics

A particle's position is given by $\vec{r}(t) = (t^3 - 2t)\hat{i} + (3t^2)\hat{j}$, where $t$ is in seconds and $\vec{r}$ is in meters. What is the magnitude of the acceleration at $t = 2 s$?

A projectile is launched horizontally from a height $h$ above the ground with an initial velocity $v_0$. If the initial height $h$ is doubled, how does the time of flight change?

A ball is thrown horizontally from the top of a building with a speed of 10 m/s. If it hits the ground 2 seconds later, what is the horizontal distance it travels before hitting the ground?

A vector has a magnitude of 10 units and makes an angle of 60° with the x-axis. What is the x-component of the vector?

A projectile is launched with an initial velocity of 30 m/s at an angle of 45^circ above the horizontal. What is the horizontal displacement of the projectile after 2 s, assuming no air resistance?

A particle moves in the x-y plane with an initial velocity of $\vec{v_0} = (5\hat{i} + 3\hat{j}) m/s$ and a constant acceleration of $\vec{a} = (-2\hat{i}) m/s^2$. What is the x-component of the particle's velocity after 4 s?

A particle moves in the x-y plane. At a certain instant, its velocity is $\vec{v} = (4\hat{i} + 3\hat{j}) m/s$ and its acceleration is $\vec{a} = (-2\hat{i} + \hat{j}) m/s^2$. At this instant, is the particle's speed increasing or decreasin...

A projectile is launched horizontally with an initial speed $v_0$ from a height $h$ above the ground. What is the range of the projectile?

A projectile is launched with an initial velocity of 20 m/s at an angle of 60° above the horizontal. What is the maximum height reached by the projectile, assuming air resistance is negligible and $g = 9.8 m/s^2$?

The velocity of a particle moving in the x-y plane is given by $\vec{v}(t) = (2t^2)\hat{i} + (3t)\hat{j}$, where $t$ is in seconds and $\vec{v}$ is in m/s. What is the magnitude of the acceleration vector at $t = 2 s$?