# math

posted by .

The velocity function is v(t) = t^2 - 6 t + 8 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,6].

• math -

v=ds/dt

ds/dt=t^2-6t+8

ds=(t^2-6t+8)*dt

s=integral(t^2-6t+8)*dt

s=(t^3-9t^2+24t)/3+C

s=(t/3)*(t^2-9t+24)+C

s=(t/3)*[(t-9)*t+24)]+C

s=Definite integral betwen(-1,6)

s=(6/3)*[(6-9)*6+24]-(-1/3)*[(-1-9)*(-1)+24]

s=(6/3)*[(-3)*6+24]+(1/3)*[-10*(-1)+24]

s=2*(-18+24)+(1/3)*(10+24)

s=2*6+(1/3)*34
s=12+34/3

s=(36/3)+(34/3)

s=70/3

## Similar Questions

1. ### Math: Calculus

The velocity function is v(t)= t^2-5t+ 4 for a particle moving along a line. The position function s(t) is an antiderivative of the velocity function. Find the displacement, s(6) - s(-3), by the particle during the time interval [-3,6].
2. ### Calculus-particle motion

1. A particle is moving on the x-axis (or any number line) Its position x(t), or distance from the origin, at the time t is given by x(t)=4t^3-16t^2+15t. t is greater than or equal to 0 a.) Where is the particle when it is at rest?
3. ### Calculous

A particle moves along the c-axis so that at time t its position is given by x(t)=t^2-6^t+9t+11 a)What is the velocity of the particle at t=0 b)During what time intervals is the particle moving to the left?
4. ### calculus

The velocity function is v(t) = - t^2 + 4 t - 3 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-2,6].
5. ### Calculus

The velocity function is v(t)=t^2-5t+6 for a particle moving along a line. Find the displacement of the particle during the time interval [-3,6].
6. ### math

The velocity function (in meters per second) for a particle moving along a line is given by v(t)=t3–4t2. Find the displacement and the distance traveled by the particle during the time interval [-1,6]. (Hint: Draw a graph of the …
7. ### Calculus (math)

The velocity function (in meters per second) for a particle moving along a line is given by v(t)=t3−5t2. Find the displacement and the distance traveled by the particle during the time interval [-1,6]. Distance traveled = ?
8. ### Calc 1

The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t^2 − 2t − 15, 1 ≤ t ≤ 7 (a) Find the displacement. (b) Find the distance traveled by the particle during the …
9. ### Calculus 1

The acceleration function (in m/s^2) and the initial velocity are given for a particle moving along a line. a(t)=t+4, v(0)=4, 0 ≤ t ≤ 11 (a) Find the velocity at time t. (b) Find the distance traveled during the give time …
10. ### Calculus

The velocity function is v(t)=t^2−5t+4 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,5]. So I found the antiderivative of the function, which gave …

More Similar Questions