Question

An object moves along the x axis according to the equation

x = 3.20t² − 2.00t + 3.00,

where x is in meters and t is in seconds.

1) Determine the average speed between t = 2.10 s and t = 3.40 s

2) Determine the instantaneous speed at t = 2.10 s.

3) Determine the instantaneous speed at t = 3.40 s.

4) Determine the average acceleration between t = 2.10 s and t = 3.40 s.

5) Determine the instantaneous acceleration at t = 2.10 s.

6) Determine the instantaneous acceleration at t = 3.40 s.

7) At what time is the object at rest?

Answer 1

given

x = 3.20t² − 2.00t + 3.00

1)

t = 2.10 s t = 3.40 s

at t = 2.1 s

x₁ = 3.20 X 2.1² − 2.00 X 2.1 + 3.00

x₁ = 12.912 s

at t = 3.4 s

x₂ = 3.20 X 3.4² − 2.00 X 3.4 + 3.00

x₂ = 33.192 s

V_avg = x₂ - x₁ / dt

= 33.192 - 12.912 / ( 3.4 - 2.1 )

V_avg = 15.6 m/s

2)

at t = 2.1 s

v₁ = dx/dt

= 6.4 t - 2

v₁ = 11.44 m/s

3 )

t = 3.4 s

v₂ = dx/dt

= 6.4 t - 2

v₂ = 19.76 m/s

4 )

a_avg = v₂ - v₁ / dt

= 19.76 - 11.44 / ( 3.4 - 2.1 )

a_avg = 6.4 m/sec²

5 )

a₁ = dv/dt

= 6.4 / 2.1

a₁ = 3.047 m/sec²

6 )

a₂ = dv/dt

= 6.4 / 3.4

a₂ = 1.882 m/sec²  

7 )

v = 6.4 t - 2

v = 0

6.4 t = 2

t = 0.3125 sec