Question

A particle moves along the x-axis according to the equation x(t) = 2.0 − 4.0t² m. What are the velocity and acceleration at t = 2.0 s and t = 5.0 s?

a) v(2.0s)=−16.0m/s, a(2.0s)=−8.0m/s
b) v(5.0s)=−40.0m/s, a(5.0s)=−8.0m/s
c) v(2.0s)=−16.0m/s, a(2.0s)=8.0m/s
d) v(5.0s)=−40.0m/s, a(5.0s)=8.0m/s

Answer 1

The velocity of the particle is -16.0 m/s at t = 2.0 s and -40.0 m/s at t = 5.0 s. The acceleration of the particle is -8.0 m/s² at both t = 2.0 s and t = 5.0 s.

Step-by-step explanation:

To find the velocity of the particle at a specific time, we take the derivative of the position function. In this case, we have x(t) = 2.0 - 4.0t². Taking the derivative of x(t) with respect to t, we get v(t) = -8.0t. To find the velocity at t = 2.0 s and t = 5.0 s, we substitute the values into the velocity function. We find that v(2.0 s) = -16.0 m/s and v(5.0 s) = -40.0 m/s.

To find the acceleration at a specific time, we take the second derivative of the position function. In this case, the second derivative is a constant, a(t) = -8.0 m/s². The acceleration does not depend on time and remains the same for all values of t. Therefore, a(2.0 s) = -8.0 m/s² and a(5.0 s) = -8.0 m/s².