A small $8.00$-kg rocket burns fuel that exerts a time-varying upward force on the rocket (assume constant mass) as the rocket moves upward from the launch pad. This force obeys the equation $F=A+B{t}^2$. Measurements show that at $t=0$, the force is $100.0$ N, and at the end of the first $2.00$ s, it is $150.0$ N. Find the constants $A$ and $B$, including their SI units.

A hockey puck with mass $0.160$ kg is at rest at the origin ($x = 0$) on the horizontal, frictionless surface of the rink. At time $t = 0$ a player applies a force of $0.250$ N to the puck, parallel to the $x$-axis; she continues to apply this force until $t = 2.00$ s. If the same force is again applied at $t=5.00$ s, what are the position and speed of the puck at $t=7.00$ s?

At the surface of Jupiter's moon Io, the acceleration due to gravity is $g=1.81$ m/s². A watermelon weighs $44.0$ N at the surface of the earth. What is the watermelon's mass on the earth's surface?

A $4.50$-kg experimental cart undergoes an acceleration in a straight line (the $x$-axis). The graph in Fig. E$4.13$ shows this acceleration as a function of time. During what times is the net force on the cart a constant?

A $4.50$-kg experimental cart undergoes an acceleration in a straight line (the $x$-axis). The graph in Fig. E$4.13$ shows this acceleration as a function of time. Find the maximum net force on this cart. When does this maximum force occur?

At the surface of Jupiter's moon Io, the acceleration due to gravity is $g = 1.81$ m/s². A watermelon weighs $44.0$ N at the surface of the earth. What would be its mass and weight on the surface of Io?

An astronaut's pack weighs $17.5$ N when she is on the earth but only $3.24$ N when she is at the surface of a moon. What is the acceleration due to gravity on this moon?