GP. A speedboat increases it's speed uniformly from V1=20.0m/s to Vf=30.0m/s in a distance of 200X10^2m. (a) Draw a coordinate system for this situation and label the relevant quantities, including vectors. (b) For the given information, what single equation is most appropriate for finding the acceleration? (c) Solve the equation selected in part (b) symbolically for the boat's acceleration in terms of Vf,V1, and delta x. (d) Substitute given values, obtaining that acceleration. (e) Find the time it takes the boat to travel the given distance.
I suspect that the distance was either
200m or 2.00*10^2m
If that's so, then the acceleration
a = ∆v/t = 10/t
the distance is
s = 20t + 1/2 at^2 = 20t + 5t = 25t = 200
so, t = 8s
I think it should be easy now to answer the questions.
University hargeisa
(a) To draw a coordinate system for this situation, we can use a simple Cartesian coordinate system with x and y axes. Since we are dealing with motion in a straight line, we can place the x-axis horizontally to represent the direction of the boat's motion. The y-axis can be vertical. Label the initial velocity as V1, final velocity as Vf, acceleration as a, and the distance traveled as Δx (200x10^2m).
(b) To find the acceleration, we can use the kinematic equation that relates final velocity, initial velocity, acceleration, and distance:
Vf^2 = V1^2 + 2aΔx
(c) Solving the equation selected in part (b) symbolically for acceleration, we get:
a = (Vf^2 - V1^2) / (2Δx)
(d) Substitute the given values:
a = (30.0^2 - 20.0^2) / (2 * 200x10^2)
Calculating this expression will give you the acceleration in a numerical value.
(e) To find the time it takes the boat to travel the given distance, we can use the equation of motion that relates initial velocity, final velocity, acceleration, and time:
Δx = V1t + (1/2)at^2
Since the boat starts from rest (V1 = 0), the equation simplifies to:
Δx = (1/2)at^2
Rearranging the equation, we can solve for time:
t = sqrt((2Δx) / a)
Substitute the given values of Δx and the acceleration you obtained earlier to find the time it takes for the boat to travel the given distance.