Question

A test rocket is launched vertically from ground level (y=0), at time t=0.0s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has to 49m and acquired velocity of 30m/s. How long the burn phase last?

A. 2.6
B. 2.3
C. 3.3
D. 3.6
E. 2.9

Answer 1

From the definition of average velocity,

`\bar v=(\Delta y)/(\Delta t)=\frac{49\,\mathrm m}t`,

and the fact that constant acceleration means

`\bar v=\frac{v_f+v_0}2=\frac{30\,(\mathrm m)/(\mathrm s)}2=15\,(\mathrm m)/(\mathrm s)`

we can solve for the time
`t`:

`15\,(\mathrm m)/(\mathrm s)=\frac{49\,\mathrm m}t\implies t=3.3\,\mathrm s`