Question

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Answer 1

a) 20 m/s²

b) 0

Explanation:

average acceleration is, Vₙ - vₓ / Δt

where, Vₙ stands for final velocity,

Vₓ stands for initial velocity, and

Δt stands for change in time

according to the question,

for t₂, s = 2³ - 2² - 2 - 2 = 8 - 4 - 4 = 0

for t₄, s = 4³ - 4² - 4 - 2 = 64 - 16 - 8 = 64 - 24 = 40

substituting the values in the formulae,

average acceleration = 40 - 0 / 4 - 2 = 40/2 = 20 m/s²

when the velocity is 0 it indicates that acceleration will also be 0

Answer 2

• Answer:

A - The Average Acceleration Between:

T = 2 and T = 4 is 16 m/s^2

B - The Acceleration When the Velocity is: Zero (0) is 0 m/s^2 at

T = 1/3 and 4 m/s^2 at T = 1

• Explanation:

• Make A Plan:
• We need to find the Average Acceleration between T = 2 and T = 4, and The Acceleration When the Velocity is Zero (0). First, We need to find the velocity function and the acceleration function.

• 1) - Solve the Problem:
• Given Distance Function:

s(t) = t^3 - t^2 - t - 2

• 2) - Find the velocity function by taking the first derivative of the distance function with respect to (T):

v(t) = d/dt(t^3 - t^2 - t - 2 ) = 3t^2 - 2t - 1

• 3) - Find the acceleration function by taking the first derivative of the velocity function with respect to (T):

a(t) = d/dt(3t^2 - 2t - 1 ) = 6t - 2

• A) - To find the average Acceleration Between T = 2 and T = 4, We need to find the acceleration at T = 2 and T = 4, and then find the average of these two values.

a(2) = 6(2) - 2 = 10

a(4) = 6(4) - 2 = 22

• Average Acceleration

= a(2) + a(4)/2

= 10 + 22/2

= 16

• B) - To find the Acceleration When the Velocity is Zero (0), We need to find the Time (T) When V(T) = 0

3t^2 - 2t - 1 = 0

• Solve the quadratic Equation for (T):

t = 1/3, 1

• Now find the Acceleration at these times:

a(1/3) = 6(1/3) - 2 = 0

a(1) = 6(1) - 2 = 4

• Draw the conclusions:

A - The Average Acceleration Between T = 2 and T = 4 is 16 m/s^2

B - The Acceleration When the Velocity is Zero (0) is 0 m/s^2 at

T = 1/3 and 4 m/s^2 at T = 1

I hope this helps you!