A short-answer or multiple-choice question asking for acceleration at a specific time or as a general expression, obtained by differentiating a given velocity or twice-differentiating a given position function.
The distance travelled by a body moving along a line in time $t$ is proportional to $t^{3}$. The acceleration-time $(a, t)$ graph for the motion of the body will be (1) [graph 1] (2) [graph 2] (3) [graph 3] (4) [graph 4]
A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\frac{dM(t)}{dt} = bv^2(t)$, where $v(t)$ is its instantaneous velocity. The instantaneous acceleration of the satellite is: (1) $-bv^3(t)$ (2) $\frac{-bv^3}{M(t)}$ (3) $-\frac{2bv^3}{M(t)}$ (4) $-\frac{bv^3}{2M(t)}$