III Careful measurements have been made of Olympic sprinter in the 100 meter dash. A quite realistic model is that the sprinter's velocity is given by v x = a 1 − e − b t where t is in s, v x is in m/s, and the constants a and b are characteristic of the sprinter. Sprinter Carl Lewis's run at the 1987 World Championships is modeled with a = 11.81 m/s and b = 0.6887 s − 1 What was Lewis's acceleration at t = 0 s, 2.00 s, and 4.00 s? Find an expression for the distance traveled at time t. Your expression from part b is a transcendental equation, meaning that you can't solve it for t. However, it's not hard to use trial and error to find the time needed to travel a specific distance. To the nearest 0.01 s, find the time Lewis needed to sprint 100.0 m. His official time was 0.01 s more than your answer, showing that this model is very good, but not perfect.
III Careful measurements have been made of Olympic sprinter in the 100 meter dash. A quite realistic model is that the sprinter's velocity is given by v x = a 1 − e − b t where t is in s, v x is in m/s, and the constants a and b are characteristic of the sprinter. Sprinter Carl Lewis's run at the 1987 World Championships is modeled with a = 11.81 m/s and b = 0.6887 s − 1 What was Lewis's acceleration at t = 0 s, 2.00 s, and 4.00 s? Find an expression for the distance traveled at time t. Your expression from part b is a transcendental equation, meaning that you can't solve it for t. However, it's not hard to use trial and error to find the time needed to travel a specific distance. To the nearest 0.01 s, find the time Lewis needed to sprint 100.0 m. His official time was 0.01 s more than your answer, showing that this model is very good, but not perfect.
III Careful measurements have been made of Olympic sprinter in the 100 meter dash. A quite realistic model is that the sprinter's velocity is given by
v
x
=
a
1
−
e
−
b
t
where t is in s, vxis in m/s, and the constants a and b are characteristic of the sprinter. Sprinter Carl Lewis's run at the 1987 World Championships is modeled with a = 11.81 m/s and
b
=
0.6887
s
−
1
What was Lewis's acceleration at t = 0 s, 2.00 s, and 4.00 s?
Find an expression for the distance traveled at time t.
Your expression from part b is a transcendental equation, meaning that you can't solve it for t. However, it's not hard to use trial and error to find the time needed to travel a specific distance. To the nearest 0.01 s, find the time Lewis needed to sprint 100.0 m. His official time was 0.01 s more than your answer, showing that this model is very good, but not perfect.
III.
The velocity-time graph of a particle in one dimension is shown in the figure.
Assuming that the particle started at x0 = 0 m, what are the instantaneous position x(t) and velocity v(t) equations (in the form compliant with SI units) that correspond to the interval
- from A to B?
- from B to D?
- from D to E?
Roughly sketch the corresponding a-t and p-t ploots for the given v-t plot.
3.) This is differential Calculus subject.
A PARTICLE IS MOVING ALONG A HORIZONTAL LINE ACCORDING TO THE GIVEN EQUATION.The Equation is S = t^3 - 9t^2 + 15t ; t>=0.where (s) meters is the directed distance of the particle from the originat (t) seconds. where (v) meters per second is the instantaneous acceleration of the particle.
1. FIND (v) AND (a) IN TERMS OF (t).2. MAKE A TABLE THAT GIVES A Description of THE POSITION AND MOTION of the particle, include in the table the intervals of time when the PARTICLE IS MOVING TO THE LEFT AND RIGHT include in the table when the VELOCITY IS INCREASING AND DECREASING include in the table when the SPEED IS INCREASING AND DECREASING include in the table the POSITION OF THE PARTICLE with respect to the origin during these intervals of time. and Show the BEHAVIOR OF THE MOTION
1c. A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v0 = 18.5 m/s. The cliff is h = 20.0 m above a flat, horizontal beach as shown in the figure.
Write the equations for the x- and y-components of the velocity of the stone with time. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not include units in your answer.)
vx=
vy=
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