The velocity function (in meters per second) for a particle moving along a line

Question

The velocity function (in meters per second) for a particle moving along a line is given by v(t) = t3 ?3t2. Find the displacement and the distance traveled by the particle during the time interval [-1,4] .(Hint: Draw a graph of the velocity function.) Your answers require that you enter the correct units.

The velocity function (in meters per second) for a particle moving along a line is given by v ( t ) = t3 - 3 t2. Find the displacement and the distance traveled by the particle during the time interval [-1, 4]. (Hint: Draw a graph of the velocity function.) Your answers require that you enter the correct units. Displacement = Distance traveled =

Explanation / Answer

here ds/dt = v.

so as v= t^3- 3t^2 we have ds/dt= t^3- 3t^2

so when we integrate both sides of ds=(t^3- 3t^2)dt

we get s= (t^4)/4-t^3

so displacement will be from -1 to 4 which is

(4^4/4 - 4^3)- ((-1)^4/4 - (-1)^3) = 0-(1/4+1)= -1.25m

distance will be calculate by using the same formula at every point.

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