ds/dt = v = 3t^2 - 24t + 36
Therefore V at t = 0 ,
V = 36 m/sec
a = dv/dt = 6t - 24
Therefore a at t = 0 ,
a = -24 m/sec^2
Distance traveled = s(3) - s(0) = 3^3-12*3^2+36*3 =27 m
at time t, the position of a body moving along the s-axis is s=t^3-12t^2+36t m. find the totaldistance traveled by the body from t=0 to t=3
S The function s = 12 - 91? + 27t, Osts 4, gives the position of a body moving on a coordinate line, with sin meters and t in seconds. a. Find the body's displacement and average velocity for the given time interval b. Find the body's speed and acceleration at the endpoints of the interval. c. When, if ever, during the interval does the body change direction? 3.4.7 At time t, the position of a body moving along the...
For each of the velocity-time graphs shown below, draw the corresponding acceleration- time graph. 2-0 0 2 46 8 I time (s) i time (s) I i time (s) 0 0 0 2 4 6 8 0 2 468 time (s) time (s) time (s) A car moves along a line (the positive x-axis). Fill in the table below with the sign (t or-) of the velocity and acceleration of the car for each of the motions described. 2 Acceleration...
A particle is moving with acceleration a(t) 36t +16. its position at time t0 is s(0) 12 and its velocity at timet0 is (0)-1. What is its position at time t- 12? Preview
A particle is moving with acceleration a(t) 36t +16. its position at time t0 is s(0) 12 and its velocity at timet0 is (0)-1. What is its position at time t- 12? Preview
The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t) t 4 5, 0sts 10 v(0) (a) Find the velocity at time t. 2 4t5 2 v(t) m/s (b) Find the distance traveled during the given time interval. 416.6 Need Help? Talk to a Tutor Read It Watch It
The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t) t 4 5,...
Let s(t) represent the position, v(t) represent the velocity, and a(t) represent the acceleration of a particle moving along a horizontal line. For each of the problems below: a. Find the net distance traveled in the interval given. Justify your answer analytically b. Find the total distance traveled in the interval given. Justify your answer analytically. v(t) = t^2 – 5t + 6 where 0 ≤ t ≤ 3.
1. At time t, the position of a body moving along the s-axis is s= t3 – 9t2 +24t m. Give formulas for the body’s velocity and acceleration at time t. Find the body’s acceleration each time the velocity is zero. Find the body’s speed each time the acceleration is zero.
13. Find the magnitudes of the initial (at t 0) velocity and acceleration of the auto respectively At time t 0 a car has a velocity of 16 m/s. It slows down with an acceleration given by -0.50t, in m/s2 for t in seconds 14. Find the time when it stops 15. Find the distance it has traveled tt the end of 4.0 s 16. Find the distance it has traveled by the time it stops
The acceleration function (in
) and initial velocity for a particle moving along a line is given
by
(a) Find the velocity (in m/s) of the particle at time
.
Velocity = meters
(b) Find the total distance traveled (in meters) by the
particle.
Total distance traveled = meters
mls2
Problem #1 (35 Points) Given The velocity of a particle as it moves along a straight line is given by v (-12+36t-6t2) ft/s, where t is in seconds. At the initial condition ( 0), so 2 ft. Find a) The acceleration of the particle as a function of time. b) The acceleration of the particle when -6 seconds. c) The position of the particle as a function of time. d) The position of the particle when -6 seconds. e) The...