A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x(t) = bt2 - ct3, where b = 2.60 m/s2 and c = 0.150 m/s3.
(a) Calculate the average velocity of the car for the time interval t = 0 to t = 8.0 s.
m/s
(b) Calculate the instantaneous velocity of the car at the following times:
i) t = 0
m/s
ii) t = 4.0 s
m/s
iii) t = 8.0 s
m/s
(c) How long after starting from rest is the car again at rest
To calculate the average velocity of the car, we need to find the displacement of the car during the time interval t = 0 to t = 8.0 s and divide it by the time interval.
(a) Average Velocity:
The displacement of an object is given by the difference in position between the final and initial positions. Here, the final position is x(t=8.0s) and the initial position is x(t=0).
x(t=8.0s) = b(8.0)^2 - c(8.0)^3
x(t=0) = b(0)^2 - c(0)^3
Substituting the values of b and c, we can calculate the displacements. Let's denote the displacements as Δx.
Δx = x(t=8.0s) - x(t=0)
Average velocity = Δx / Δt, where Δt = 8.0s - 0
(b) Instantaneous Velocity:
The instantaneous velocity of the car can be found by taking the derivative of the position function, x(t), with respect to time, t.
Differentiating x(t) = bt^2 - ct^3 with respect to t, we get:
v(t) = 2bt - 3ct^2
To find the instantaneous velocity at specific times:
i) t = 0: Substitute t = 0 in v(t) = 2bt - 3ct^2.
ii) t = 4.0s: Substitute t = 4.0 in v(t) = 2bt - 3ct^2.
iii) t = 8.0s: Substitute t = 8.0 in v(t) = 2bt - 3ct^2.
(c) Time when the car is again at rest:
To find the time when the car is at rest, we need to find the value of t when the velocity function v(t) equals zero.
Setting v(t) = 0, we can solve the equation 2bt - 3ct^2 = 0 for t.
a pendulum has a period on the earth of 1.35s.what is its period on the surface of the moon where g=1.62m/s^2
a) average velocity= (x(8)-x(0))/8
b) v(t)=x'(t)=2bt-3ct^2
Put t=0;4;8 and calculate. I assume you know calculus to get v(t)=x'(t)
You can do this yourself.
Please use ^ before exponents.
For average velocity, compute
x at 0 and 8 s and divide by the elapsed time, 8s
For instantaneous velocity, take the derivative dx/dt at each of the times listed.