The estimated instantaneous velocity of the ship at t=4 hours is approximately 20.00mi./h., which corresponds to option A.
To estimate the instantaneous velocity at t=4 hours, you can use the concept of average velocity over a small time interval. The instantaneous velocity is essentially the limit of the average velocity as the time interval approaches zero.
The average velocity avg_v over a small time interval Δt is given by the formula:
v_avg = Δs/Δt
where
Δs is the change in displacement and
Δt is the change in time.
In this case, you can use the data for t=3.99 hours and t=4.00 hours to estimate the instantaneous velocity
Δs=s(4.00)−s(3.99)
Δt=4.00−3.99
Calculate these values:
Δs=32.00−31.80=0.20miles
Δt=4.00−3.99=0.01hours
Now, calculate the average velocity:
v_avg = 0.20/0.01 =20.00mi./h.
So, the estimated instantaneous velocity of the ship at t=4 hours is approximately 20.00mi./h., which corresponds to option A.