1. Jasmine rode a horse down a path headed north. she started from rest and then accelerated at 0.5 m/s2 for 12 seconds and then travelled at a constant speed for 28 seconds.
a.) what was her velocity after 12 seconds?
b.) what was jasmines displacement after 10 seconds?
c.) how far did Jasmine travel during her 40 s ride?
d.) draw a velocity time graph for her motion
2. Bryce can ride his bicycle at an average speed of 18 m/s and Ally rides with an average speed of 23 m/s. ally gives bryce a 200 m Headstart in a 1 km (1000m) race. use a distance time graph to solve the following questions:
a.) who wins the race? explain your answer
b.) how many meters separate the 2 cyclists at the end of the race?
1.
a.)
Vf=Vi +at
Where
Vf=?
Vi=0m/s
a=0.5m/s^s
t=12s
Solve for Vf:
Vf=0m/s +(0.5m/s^2)*(12s)
Vf=6m/s
b.)
d=Vi*t + 1/2at^2
Where
d=?
Vi=0m/s
a=0.5m/s^s
t=10s
Solve for d:
d=0m/s*(12s) + 1/2(0.5m/s^2)(10s)^2
d=0 +25m
d=25m
c.)
d=Vi*t + 1/2at^2
Where
d=?
Vi=0m/s
a=0.5m/s^s
t=40s
Solve for d:
d=0m/s*(12s) + 1/2(0.5m/s^2)(40s)^2
d=0 +400m
d=400m
d.)
Plot distance Vs velocity
x axis =displacement and y=velocity
2.
****Plot distance on the x-axis and time (distance/velocity) on the y-axis.
***Remember, Bryce only has to travel 800m.
a.)
d=r*t
Where
r=velocity
t=?
and
d=displacement.
Bryce
d=800m
r=18m/s
t=?
800=18m/s*t
t=800m/18m/s
t=44.4s
Ally
d=1,000m
r=23m/s
t=?
1,000m=23m/s*t
t=1,000m/23m/s
t=43.5s
Ally wins.
b.)
Bryce wins the race in 43.4s. How far is Ally from the finish line when Bryce reaches the finish line?
d=18 m/s*43.4s
d1=781.2m
Total distance=d1+d2=781.2m + 200m=981.2m
1,000m-981.2m=18.8m=19.0m is the distance that separates them when the race ends.
Typo correction. Look for ^&***" for correction .
1.
a.)
Vf=Vi +at
Where
Vf=?
Vi=0m/s
a=0.5m/s^s
t=12s
Solve for Vf:
Vf=0m/s +(0.5m/s^2)*(12s)
Vf=6m/s
b.)
d=Vi*t + 1/2at^2
Where
d=?
Vi=0m/s
a=0.5m/s^s
t=10s
Solve for d:
d=0m/s*(12s) + 1/2(0.5m/s^2)(10s)^2
d=0 +25m
d=25m
c.)
d=Vi*t + 1/2at^2
Where
d=?
Vi=0m/s
a=0.5m/s^s
t=40s
Solve for d:
d=0m/s*(12s) + 1/2(0.5m/s^2)(40s)^2
d=0 +400m
d=400m
d.)
Plot distance Vs velocity
x axis =displacement and y=velocity
2.
****Plot distance on the x-axis and time (distance/velocity) on the y-axis.
***Remember, Bryce only has to travel 800m.
a.)
d=r*t
Where
r=velocity
t=?
and
d=displacement.
Bryce
d=800m
r=18m/s
t=?
800=18m/s*t
t=800m/18m/s
t=44.4s
Ally
d=1,000m
r=23m/s
t=?
1,000m=23m/s*t
t=1,000m/23m/s
t=43.5s
Ally wins.
b.)
^&***" Ally wins the race in 43.4s. How far is Bryce from the finish line when Ally reaches the finish line?" ***^&
d=18 m/s*43.4s
d1=781.2m
Total distance=d1+d2=781.2m + 200m=981.2m
1,000m-981.2m=18.8m=19.0m is the distance that separates them when the race ends.
Thank u so much :)
To answer these questions, we need to understand the basic equations of motion and how to interpret and analyze different types of graphs.
1. Jasmine's Motion:
a.) To calculate Jasmine's velocity after 12 seconds, we need to use the equation:
Final velocity (v) = Initial velocity (u) + Acceleration (a) * Time (t)
Given:
Initial velocity (u) = 0 (since Jasmine starts from rest)
Acceleration (a) = 0.5 m/s^2
Time (t) = 12 seconds
Plug in the values:
v = 0 + (0.5 m/s^2 * 12 s)
v = 6 m/s
b.) To calculate Jasmine's displacement after 10 seconds, we need to split her motion into two parts: acceleration and constant speed.
From the question, we know that she accelerates for 12 seconds and then travels at a constant speed for the remaining 28 seconds.
Displacement (s) during acceleration can be calculated using the equation:
s = (u * t) + (0.5 * a * t^2)
Given:
Initial velocity (u) = 0 (since Jasmine starts from rest)
Acceleration (a) = 0.5 m/s^2
Time (t) = 10 seconds
Plug in the values:
s1 = (0 * 10) + (0.5 * 0.5 * 10^2)
s1 = 25 m
Displacement (s) during constant speed can be calculated using the equation:
s = v * t
Given:
Velocity (v) = 6 m/s (we calculated this in part a)
Time (t) = 28 seconds
Plug in the values:
s2 = 6 * 28
s2 = 168 m
Total displacement = s1 + s2
Total displacement = 25 + 168
Total displacement = 193 m
c.) To calculate how far Jasmine traveled during her 40-second ride, we simply need to find the displacement during the entire duration.
Total displacement = s1 + s2 (calculated in part b)
Total displacement = 193 m
d.) To draw a velocity-time graph, we first need to understand that velocity is the rate at which displacement changes with time. Since acceleration is constant during the first 12 seconds, the velocity-time graph will show a straight line inclined at an angle of 0.5 m/s^2 for the first 12 seconds. After that, the velocity will remain constant, resulting in a horizontal line for the remaining 28 seconds.
2. Bryce and Ally's Race:
a.) To determine who wins the race, we need to look at the respective distances covered by each cyclist.
From the information given, Bryce has a head start of 200 m, so he starts ahead of Ally.
Distance covered by Bryce = 200 m
Distance covered by Ally = 0 m
Now, let's analyze their distances covered over time using a distance-time graph.
The slope of the graph represents the speed of each cyclist.
Since Bryce's average speed is 18 m/s, his line on the graph will be less steep than Ally's line, whose average speed is 23 m/s.
By comparing the slopes of the lines, we can determine who crosses the finish line first. The cyclist with the steeper slope will win the race.
b.) To find the distance separating the two cyclists at the end of the race, we need to calculate the difference in distance covered.
Distance covered by Bryce = 1000 m (1 km - the total race distance)
Distance covered by Ally = 1000 m
The difference in distance will give us the separation between them at the end of the race:
Separation at the end = Distance covered by Bryce - Distance covered by Ally
Separation at the end = 1000 m - 1000 m
Separation at the end = 0 m
Therefore, there is no separation between the two cyclists at the end of the race, as they will cross the finish line simultaneously.