To evaluate the acceleration of the model rocket at the given times, we can use the relationship between velocity and time and the fact that acceleration is the derivative of velocity with respect to time. The formula for acceleration as a function of time is:
a(t) = dv(t)/dt
Where:
- a(t) is the acceleration at time t.
- v(t) is the velocity at time t.
We're given the velocity at various times: v(0.0s) = 0 m/s, v(1.0s) = 36 m/s, v(2.0s) = 27 m/s. We can use this information to calculate the acceleration at those times.
1. At t = 0.0s:
a(0.0s) = dv(0.0s)/dt
Since v(0.0s) = 0 m/s, the acceleration at t = 0.0s is also 0 m/s².
2. At t = 1.0s:
a(1.0s) = dv(1.0s)/dt
Given that v(1.0s) = 36 m/s, and we know the velocity at t = 0.0s is 0 m/s, we can calculate the acceleration as follows:
a(1.0s) = (v(1.0s) - v(0.0s)) / (1.0s - 0.0s) = (36 m/s - 0 m/s) / 1.0s = 36 m/s².
3. At t = 2.0s:
a(2.0s) = dv(2.0s)/dt
Given that v(2.0s) = 27 m/s, and we know the velocity at t = 1.0s is 36 m/s, we can calculate the acceleration as follows:
a(2.0s) = (v(2.0s) - v(1.0s)) / (2.0s - 1.0s) = (27 m/s - 36 m/s) / 1.0s = -9 m/s².
So, the acceleration of the model rocket at the specified times is as follows:
- At t = 0.0s: 0.0 m/s²
- At t = 1.0s: 36 m/s²
- At t = 2.0s: -9 m/s²