____________________________________________________________________________
A speedboat increases its speed uniformly from 20 m/s to 30 m/s in a distance of 200m. Find
(a) the magnitude of its acceleration and
(b) the time it takes the boat to travel the 200-m distance.
This is the motion with constant acceleration. We can use the following equation to find the
magnitude of acceleration
where
_________________________________________________________________
A ball is thrown vertically upward with a speed of 25.0m/s.
(a) How high does it rise?
(b) How long does it take to reach its highest point?
(c) How long does the ball take to hit the ground after it reaches its highest point?
(d) What is its velocity when it returns to the level from which it started?
This is the motion with constant acceleration (free fall acceleration).
(a) We need to use the following equation (the initial velocity is 25 m/s and the final velocity is
0):
(b) We need to use the following equation (the initial velocity is 25 m/s and the final velocity is
0):
(c) At this moment we do not know the final velocity, but we know the initial velocity (it is 0)
and we know the height (the traveled distance) – it is 31.9 m. Then we can use the following
equation:
From this equation we can find time:
It is the same time as in part (b).
(d) Now we can find the final velocity (the magnitude):
__________________________________________________________________
A boy walks to the store using the following path: 0.4 miles west, 0.2 miles north, 0.3 miles east.
What is his total displacement? That is, what is the length and direction of the vector that points
from her house directly to the store?
Solution:
The net displacement is the vector sum of three displacements as shown in the figure. It is more
easier to find the net displacement in terms of components: x component (along east direction), y
component (along north direction).
x component = x component of the first displacement + x component of the second displacement
+ x component of the third displacement = -0.4 + 0 + 0.3 = -0.1 miles.
y component = y component of the first displacement + y component of the second displacement
+ y component of the third displacement = 0 + 0.2 + 0 = 0.2 miles.
Then the magnitude of the net displacement is
The angle between the direction of the net displacement and west direction is
Then
A coin is dropped from a 400 m high tower. What is the coin's velocity when it hits the ground?
How long does it take to get there?
The minus sign means that the direction of velocity is downward.
________________________________________________________________
While you are traveling in a car on a straight road at 90 km/hr, another car passes you in the
same direction; its speedometer reads 120km/hr. What is your velocity relative to the other
driver? What is the other car's velocity relative to you?
The relative velocity is equal to the difference of velocities.
So if you need to find your relative velocity then you need to subtract from your velocity the
velocity of another car:
The minus sign here gives us the direction of relative velocity: the direction is opposite to the
directions of motions of the cars.
Similarly we can find:
The plus sign here gives us the direction of relative velocity: the direction is the same as the
directions of motions of the cars.
____________________________________________________________________
Emily takes a trip, driving with a constant velocity of 90 km/h to the north except for a 30 min
rest stop. If Emily's average velocity is 75 km/h to the north, how long does the trip take?
The average velocity is the ratio of traveled distance and the traveled time:
If the traveled time is t, then Emily traveled time (t-0.5)h with the speed 90 km/h. Then the
traveled distance is
We substitute this relation in the first equation and obtain:
Then
Then we can find L (length of the trip):
__________________________________________________________
A car going at 10 m/s undergoes an acceleration of
for 6 seconds. How far did it go when it was accelerating?
In this problem we just need to use the equation:
Then at t = 6s we have: