Question

The velocity-time graph for a two-stage rocket is shown below. Use the graph and your understanding and of slope calculations to determine the acceleration of the rocket during the following time interval.

Answer 1

a=

• 
  `40 ms^(-2) for 0\leq t\leq 1`
• 
  `20ms^(-2) for 1\leq t\leq 4`
• 
  `-20ms^(-2) for 4\leq t\leq \infty`

Explanation:

We will find the acceleration in 3 intervals of time(t) and those intervals are:

• 
  `0\leq t\leq 1`
• 
  `1\leq t\leq 4`
• 
  `4\leq t\leq\infty`

We know that acceleration(a) is given by
`a= \lim_(\Delta t \to 0) (\Delta v)/(\Delta t)`=Slope of velocity-time graph

In interval
`0\leq t\leq 1`,

`a=Slope= (\Delta v)/(\Delta t)=(40-0)/(1-0) =40ms^(-2)`

In interval
`1\leq t\leq 4`,

`a=Slope= (\Delta v)/(\Delta t)=(100-40)/(4-1) =20ms^(-2)`

In interval
`4\leq t\leq\infty`,

`a=Slope= (\Delta v)/(\Delta t)=(60-100)/(6-4) =-20ms^(-2)`