Question #111244

. An object moves along the x axis according to the equation x(t) (3.00t 2 2.00t 3.00) m, where t is in seconds. Determine (a) the average speed between t 2.00 s

and t 3.00 s, (b) the instantaneous speed at t 2.00 s

and at t 3.00 s, (c) the average acceleration between

t 2.00 s and t 3.00 s, and (d) the instantaneous acceleration at t 2.00 s and t 3.00 s.

and t 3.00 s, (b) the instantaneous speed at t 2.00 s

and at t 3.00 s, (c) the average acceleration between

t 2.00 s and t 3.00 s, and (d) the instantaneous acceleration at t 2.00 s and t 3.00 s.

Expert's answer

We have the equation of motion

"x(t)=3t^2+2t+3"

We write expressions for speed

"v(t)=\\frac{dx(t)}{dt}= \\frac{d(3t^2+2t+3 )}{dt}=6t+2"

We determine the instantaneous velocity at 2s and 3s.

"v(2)=6t+2=6 \\cdot 2+2=14 { m\/s }"

"v(3)=6t+2=6 \\cdot 3+2=20 { m\/s }"

The speed has a linear relationship, then the average speed is

"v_{average}=\\frac{v(2)+v(3)}{2}=\\frac{14+20}{2}=17 m\/s"

We write expressions for acceleration

"a(t)=\\frac{dv(t)}{dt}= \\frac{d(6t+2 )}{dt}=6m\/s^2"

To accelerate, we have

"a(2)=a(3)=a_{average}=6 m\/s^2"

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