# What is the initial acceleration of the plane? What is the acceleration of the plane at the point of take-off?

## During take-off a jet airplane of mass 10000kg can produce a maximum thrust of 40kN, At the point of take-off, the plane experiences a drag force of 20kN. a)Calculate the initial acceleration of the plane. b)Calculate the acceleration of the plane at the point of take-off.

Mar 12, 2017

Initially, the acceleration is $4 \frac{m}{s} ^ 2$. At takeoff, it is $2 \frac{m}{s} ^ 2$.

#### Explanation:

In both cases, we need to evaluate the net force acting on the plane. This net force will, according to Newton's second law, be equal to $m a$, and because we know the mass, the acceleration $a$ can be found.

Initially, the only force is the thrust of the engines, so

${F}_{\text{net}} = m a = 40 000 N$

$a = \frac{40 000}{10 000} = 4 \frac{m}{s} ^ 2$

At the point of takeoff, there is also a drag force of 20 000 N that opposes the thrust, leaving a net force of $40 000 - 20 000 = 20 000 N$

${F}_{\text{net}} = m a = 20 000 N$

$a = \frac{20 000}{10 000} = 2 \frac{m}{s} ^ 2$