If a space launch vehicle is subjected to an acceleration of 20 m/s² during liftoff and it takes 10 seconds to reach its desired velocity, the change in velocity can be calculated using the basic kinematic relation:
Change in velocity=a×t\text{Change in velocity}=a\times tChange in velocity=a×t
where a=20 m/s2a=20,\text{m/s}^2a=20m/s2 and t=10 st=10,\text{s}t=10s. So,
Δv=20×10=200 m/s\Delta v=20\times 10=200,\text{m/s}Δv=20×10=200m/s
This means the vehicle's velocity increases by 200 m/s in 10 seconds under this acceleration
Additional context on rocket acceleration:
- The acceleration of a rocket at liftoff is determined by the net force acting on it, which is the thrust minus the weight, divided by the mass of the rocket: a=T−Wma=\frac{T-W}{m}a=mT−W
- For example, the Space Shuttle had an acceleration of about 20 m/s² at launch, which is roughly 2 g's (twice the acceleration due to gravity)
- Rocket acceleration changes during flight due to decreasing mass as fuel burns and changing thrust and drag forces
In summary, with a constant acceleration of 20 m/s² over 10 seconds, the velocity change is 200 m/s.
