n object moves along the x axis according to the equation x = 3.10 t 2 2.00 t +

Question

n object moves along the x axis according to the equation

x = 3.10t2 2.00t + 3.00,

where x is in meters and t is in seconds.

(a) Determine the average speed between t = 3.50 s and t = 5.30 s.
m/s

(b) Determine the instantaneous speed at t = 3.50 s.
m/s

Determine the instantaneous speed at t = 5.30 s.
m/s

(c) Determine the average acceleration between t = 3.50 s and t = 5.30 s.
m/s2

(d) Determine the instantaneous acceleration at t = 3.50 s.
m/s2

Determine the instantaneous acceleration at t = 5.30 s.
m/s2

(e) At what time is the object at rest?
s

Explanation / Answer

x = 3.10t2 2.00t + 3.00

Velcoity = dx/dt
Velocity v = d/dt(3.10t2 2.00t + 3.00)
v = 6.2 t - 2 m/s

Acceleration = dv/dt
a = d/dt(6.2 t - 2 )
a = 6.2 m/s^2

(a)
Position at t = 5.3s
x = 3.10*5.3^2 - 2 * 5.3 + 3
x = 79.5 m

Position at t = 3.5s
x = 3.10*3.5^2 - 2 *3.5 + 3
x = 34 m

Average speed between t = 3.50 s and t = 5.30 s = (79.5 - 34) / (5.3 -3.5) m/s
Average speed = 25.7 m/s

(b)
Instantaneous speed at t = 5.30 s.
V = 6.2 * 5.3 - 2
V at t = 5.3s = 30.86 m/s

Instantaneous speed at t = 3.50 s
V = 6.2 * 3.5 - 2
V at t = 3.5s = 19.7 m/s

(c)
Average acceleration between t = 3.50 s and t = 5.30 s =
a = (30.86 - 19.7) / (5.3-3.5) m/s^2
a = 6.2m/s^2

(d)
Acceleration is constsant and therefore,
Instantaneous acceleration at t = 5.30 and t = 3.5
a = 6.2 m/s^2

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