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,

$\bar v=\dfrac{\Delta y}{\Delta t}=\dfrac{49\,\mathrm m}t$,

and the fact that constant acceleration means

$\bar v=\dfrac{v_f+v_0}2=\dfrac{30\,\frac{\mathrm m}{\mathrm s}}2=15\,\dfrac{\mathrm m}{\mathrm s}$

we can solve for the time $t$:

$15\,\dfrac{\mathrm m}{\mathrm s}=\dfrac{49\,\mathrm m}t\implies t=3.3\,\mathrm s$