A speedboat travels in a straight line and increases in speed uniformly from υ i = 20.0 m/s to υ f = 30.0 m/s in displacement Δ x of 200 m. We wish to find the time interval required for the boat to move through this displacement, (a) Draw a coordinate system for this situation, (b) What analysis model is most appropriate for describing this situation? (c) From the analysis model, what equation is most appropriate for finding the acceleration of the speedboat? (d) Solve the equation selected in part (c) symbolically for the boats acceleration in terms of υ i , υ f , and Δ x . (e) Substitute numerical values lo obtain the acceleration numerically. (f) Find the time interval mentioned above.
A speedboat travels in a straight line and increases in speed uniformly from υ i = 20.0 m/s to υ f = 30.0 m/s in displacement Δ x of 200 m. We wish to find the time interval required for the boat to move through this displacement, (a) Draw a coordinate system for this situation, (b) What analysis model is most appropriate for describing this situation? (c) From the analysis model, what equation is most appropriate for finding the acceleration of the speedboat? (d) Solve the equation selected in part (c) symbolically for the boats acceleration in terms of υ i , υ f , and Δ x . (e) Substitute numerical values lo obtain the acceleration numerically. (f) Find the time interval mentioned above.
Solution Summary: The author explains that the coordinate system for the given situation is used to show the position of the points on the axis.
A speedboat travels in a straight line and increases in speed uniformly from υi = 20.0 m/s to υf = 30.0 m/s in displacement Δx of 200 m. We wish to find the time interval required for the boat to move through this displacement, (a) Draw a coordinate system for this situation, (b) What analysis model is most appropriate for describing this situation? (c) From the analysis model, what equation is most appropriate for finding the acceleration of the speedboat? (d) Solve the equation selected in part (c) symbolically for the boats acceleration in terms of υi, υf, and Δx. (e) Substitute numerical values lo obtain the acceleration numerically. (f) Find the time interval mentioned above.
A certain physics problem about projectile motion has several parts, as listed in the questions below. For each, write out what variables (y, vy, ay, t, x, vx, etc) need to be solved for in each part, and at what event or condition, also expressed using symbols and/or known values. For example: “Find ______ (variable) when _______ (variable) equals ________.”
How long until the projectile hits the ground?
How far has the projectile travelled horizontally, when it hits the ground?
What is the projectile’s speed the moment before ithits the ground?
What is the projectile’s direction (angle) of flight, just before hitting the ground?
How long until the projectile reaches its maximum altitude?
What is that maximum altitude?
How long until the projectile reaches a wall/building standing 100 m away (horizontally)?
The equation r(t) = ( sin t)i + ( cos t)j + (t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors.
π
Then write the particle's velocity at t=
as a product of its speed and direction.
The velocity vector is v(t) = (i+j+ k.
Suppose we are told that the acceleration a of a particle moving with uniform speed ν in a circle of radius r is proportional to some power of r, say rn, and some power of ν, say νm. Determine the values of n and m and write the simplest form of an equation for the acceleration.
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