Question

Use the graph to calculate the acceleration of the rocket while the engine is working. Show all steps.

Answer 1

The acceleration of the rocket while the engine is working is 5 meters per square seconds.

Step-by-step explanation:

Since the rocket accelerates uniformly, the velocity increases linearly and the acceleration (
`a`), measured in meters per second, can be determined by definition of secant line:

`a = (v_(f)-v_(o))/(t_(f)-t_(o))` (1)

Where:

`t_(o)`,
`t_(f)` - Initial and final instants, measured in seconds.

`v_(o)`,
`v_(f)` - Initial and final velocities, measured in meters per second.

If we know that
`t_(o) = 0\,s`,
`t_(f) = 8\,s`,
`v_(o) = 0\,(m)/(s)` and
`v_(f) = 40\,(m)/(s)`, then the acceleration of the rocket while the engine is working:

`a = (40\,(m)/(s)-0\,(m)/(s) )/(8\,s-0\,s)`

`a = 5\,(m)/(s^(2))`

The acceleration of the rocket while the engine is working is 5 meters per square seconds.