Question

Calculus/physics problem? A particle is moving along the x-axis with velocity v(t)=sin2t. At time t=pi/2 it has position x = 3. Find the total distance, s traveled by this particle on the interval 0<=t<=pi.

Answer 1

if we integrate velocity we get distance
integral of sin2t =- (1/2) cos2t + c
x = -(1/2) cos 2t + c
when x = 3 t = pi/2:
so
3 = -(1/2) cos pi + c
3 = -(1/2) * -1 + c
so c = 3 - 1/2 = 2.5

so relation between distance and time is

x = -0.5 cos 2t + 2.5

Answer 2

So would I just plug in for pi and plug in for zero and subtract the 0 value from the pi value?

Answer 3

yes

Answer 4

thanks

Answer 5

yw

Answer 6

you still there?
i do apologize - i gave you the wrong information in my last post

Answer 7

the x in the formula gives you the position ( or displacement) of particle on x-axis
this is simple harmonic motion - the particle oscillates about a point on the axis.

at time 0 the displacement x = -0.5 * cos0 + 2.5 = -0.5 + 2.5 = 2
at time pi/2 (half the period) displacement = 3
at time t displacement = -0.5 * cos 2pi + 2.5 = -0.5 * 1 + 2.5 = 2
so total distance travelled = (3-2) + (3-2) = 2 units

at time pi/2 the particle is at maximum distance from center of oscillation (when cos = -1)

answer distance travelled = 2

Answer 8

I got that anyway

Answer 9

oh ok