Linear, Relative, and Circular Motion

A car travels a certain distance at an average speed of 105 km/h, taking 2 hours and 20 minutes. If the same distance is covered at an average speed of 70 km/h, what is the additional time required for the trip?

A car's distance from a traffic light is given by $x(t) = bt^2 - ct^3$, where $b = 2.40 \frac{m}{s^2}$ and $c = 0.120 \frac{m}{s^3}$. What is the average velocity of the car during the time interval from $t = 0$ to $t = 10.0$ seconds?

A car's distance from a traffic light is given by $x(t) = bt^2 - ct^3$, where $b = 2.40 \frac{m}{s^2}$ and $c = 0.120 \frac{m}{s^3}$. At what time after starting from rest will the car be at rest again?

If a human can survive a maximum acceleration of $250 \frac{m}{s^2}$, over what minimum distance must an airbag stop a person in an accident, assuming an initial speed of 105 km/h?

A 7500 kg rocket accelerates upward at $2.25 \frac{m}{s^2}$. After reaching a height of 525 m, its engines fail. What is the maximum ADDITIONAL height the rocket will reach above the point of engine failure?

A 7500 kg rocket accelerates upward at $2.25 \frac{m}{s^2}$. After reaching a height of 525 m, its engines fail. How fast will the rocket be traveling when it crashes back down to the launch pad?

A passenger train is traveling at 25.0 m/s when the engineer sees a freight train 200 m ahead traveling at 15.0 m/s in the same direction. The passenger train decelerates at a constant rate of -0.100 m/s². At what distance from the passenger train’s initial position does the collision occur, if one happens?

An object's velocity is given by $v(t) = \alpha - \beta t^2$, where $\alpha = 4.00 \frac{m}{s}$ and $\beta = 2.00 \frac{m}{s^3}$. If the object starts at $x = 0$, what is its position as a function of time?

An object's velocity is given by $v(t) = \alpha - \beta t^2$, where $\alpha = 4.00 \frac{m}{s}$ and $\beta = 2.00 \frac{m}{s^3}$. If the object starts at $x = 0$, what is its maximum positive displacement from the origin?

The acceleration of a particle is given by $a(t) = -2.00 \frac{m}{s^2} + (3.00 \frac{m}{s^3})t$. What initial velocity, $v_0$, must the particle have so that its x-coordinate at $t = 4.00$ s is the same as it was at $t = 0$?

The acceleration of a particle is given by $a(t) = -2.00 \frac{m}{s^2} + (3.00 \frac{m}{s^3})t$. If the initial conditions are set such that $x(4) = x(0)$, what is the velocity of the particle at $t = 4.0$ s?

The acceleration of a motorcycle is given by $a(t) = At - Bt^2$, where $A = 1.50 \frac{m}{s^3}$ and $B = 0.120 \frac{m}{s^4}$. If the motorcycle starts from rest at the origin, what is its velocity as a function of time?

During a rocket launch, a fuel canister is discarded at a height of 235 m. The rocket continues to accelerate upwards at $3.30 \frac{m}{s^2}$. Assuming the rocket's acceleration remains constant, how high is the rocket when the fuel canister hits the ground?

Car A's distance from the starting line is given by $x_A(t) = \alpha t + \beta t^2$ and Car B's distance is given by $x_B(t) = \gamma t^2 - \delta t^3$, where $\alpha = 2.60 \frac{m}{s}$, $\beta = 1.20 \frac{m}{s^2}$, $\gamma = 2.80 \frac{m}{s^2}$, and $\delta = 0.20 \frac{m}{s^3}$. At what time(s), $t$, will the two cars be at the same point?

A Ferris wheel with a radius of 14.0 m has a constant linear speed of 7.00 m/s. What is the magnitude of the passenger's centripetal acceleration?

A Ferris wheel with radius 14.0 m turns with a constant linear speed of 7.00 m/s. How long does it take for the Ferris wheel to make one complete revolution?

An astronaut is tested in a centrifuge with an arm length of 8.84 m. If the maximum sustained acceleration is 12.5g, what is the required speed of the astronaut's head?

An astronaut is in a centrifuge with an arm length of 8.84 m and the maximum sustained acceleration is 12.5g. If the astronaut is 2.00 m tall and aligned along the arm, what is the difference in acceleration between the astronaut's head and feet?

A 76.0 kg boulder is rolling horizontally off a 20 m high cliff. A dam is located 100 m from the base of the cliff. What is the MINIMUM speed the rock must have so that it will travel to the field without striking the dam?