Question

An aircraft has a lift-off of $120km/h.$ What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of $240m?$ (in m/s$^2$)
A. ${\text{2}}{\text{.2}}$
B. ${\text{2}}{\text{.3}}$
C. ${\text{2}}{\text{.4}}$
D. ${\text{2}}{\text{.5}}$

Answer 1

Hint: First convert the units of the given terms in the same format. So, convert kilometre per hour in metres per second. From the given terms find the unknown term acceleration from the correlation. Use the difference of the initial velocity and final velocity equation of the motion.

Complete step by step answer:
Here, the initial velocity of an aircraft be $u = 0m/s$
Final velocity of an aircraft, $v = 120km/h = \dfrac{{120 \times 1000}}{{3600}} = 33.33m/s$
Run off distance, $s = 240m$
Now, using the equation –
${v^2} - {u^2} = 2as$
Place the known values in the above equation –
${\left( {33.33} \right)^2} - {0^2} = 2a(240)$
Simplify and make unknown acceleration “a” the subject –
$
  a = \dfrac{{{{(33.33)}^2}}}{{2(240)}} \\
  a = 2.3m/{s^2} \\
 $
Therefore, the required answer is – the minimum constant acceleration $a = 2.3m/{s^2}$ aircraft requires if it is to be airborne after a takeoff run of $240m$.

So, the correct answer is “Option B”.

Note:
Remember all the three laws of motion and its equation to solve these types of word problems. Always double check the given units and units of the answer required in the solution. Always know the basic relation among the different physical parameters to convert its units. Like kilometres to metres, kilogram to gram, milli-second to second and many such relations.