# Ap Calculus

posted by .

A particle moves in a stright line and its acceleration is given by a(t)=6t+4. its initial position is s(0)=9 and its position when t=1 is s(1)=6. find the velocity of the particle when t=2.

A. v(2)=14
B. v(2)=7
C. v(2)=4
D. v(2)=9
E. v(2)=0

• Ap Calculus -

a = 6 t+4
then
v = 3 t^2 + 4 t + c
then
s = t^3 + 2 t^2 + c t + k
now find the constants c and k from the given points
s(0) = 9
9 = 0^3 + 2 0^3 + c 0 + k
so
k = 9 and we so far have
s = t^3 + 2 t^2 + c t + 9
now
s(1) = 6
6 = 1^3 + 2 (1)^2 + c (1) + 9
6 = 1 + 2 + c + 9
c = -6
so in the end
s = t^3 + 2 t^2 - 6 t + 9
I guess you can put in t = 2

• Ap Calculus -

I get an answer of 13 but it's not one of the choices

## Similar Questions

1. ### Calculus

A particle moves on a vertical line. Its position, s, in metres at t seconds is given by s(t) = t^3 - 9t^2 + 24t, t>0/ I found the velocity and acceleration functions. s'(t) = 3t^2 - 18t + 24 s''(t) = 6t-18 b) When is the particle …
2. ### HS Calculus

Having trouble with this questions. Please help. A particle moves on the x-axis so that its position at any time t (is greater than or equal to) 0 is given by x(t) = 2te^-t a) Find the acceleration of the particle at t=0 b)find the …
3. ### Calculus

a particle moves along a line so that at any time t its position is given by x(t)=2(pi)t + cos2(pi)t find velocity find acceleration what are the values of t, 0<t<3, for which the particle is at rest?
4. ### calculus

a particle moves along a number line measured in cm so that its position at time t sec is given by s=72/(t+2) +k, k is a constant and t>=0 seconds. (a) Find the instantaneous velocity of the particle at t=4 seconds (b) Find the …
5. ### physics

A particle leaves the origin with an initial velocity = (2.35 m/s) and moves with constant acceleration = (-1.90 m/s2) + (2.60 m/s2)>. (a) How far does the particle move in the x direction before turning around?
6. ### calculus

5. A particle moves along the y – axis with velocity given by v(t)=tsine(t^2) for t>=0 . a. In which direction (up or down) is the particle moving at time t = 1.5?
7. ### Calculus

The position of a particle moving on a horizontal line is given by s(t)=2t^3-15t^2+24t-5, where s is measured in feet and t in seconds. a: What is the initial position of the particle?
8. ### calculus

A particle moves on a line away from its initial position so that after t hours it is s = 6t^2 + 2t miles from its initial position. Find the average velocity of the particle over the interval [1, 4]. Include units in your answer.
9. ### physics

A particle is moving along a straight line and its position is given by the relation x=( t3-6t2-15t+40)mm. Find:- (a). The time at which velocity is zero. (b). Position & displacement of the particle at that point. (c). Acceleration …
10. ### physics

A particle is moving along a straight line and its position is given by the relation x=(t3- 6t2- 15t+40) m FIND a) The time at which velocity is Zero, b) Position and displacement of the particle at that point. c) Acceleration for …

More Similar Questions