Answer to Question #291315 in Mechanics | Relativity for ipen

Question

1. Ruel is on his way to the grocery store riding his motorcycle. He started at rest in front of their house. He then travels ahead so that his distance from where he started is given by the equation: x(t) = (2.4 m/s²) t²-(0.120 m/ s²) t³

a. Calculate the average velocity of the motorcycle for the time interval t=0 sec to t=10 sec.

b. Determine the instantaneous velocity at t=0 sec and t=5 sec

Answer 1

Explanation.

• Differentiating the given function one with respect to time gives the function for instantaneous velocity.
• Integrating a distance function with respect to time gives the total distance covered over a period.

a)

• For this part, integrate the given distance function with respect to time.
• Then you get the total distance covered during t=0 and t=10.
• Then divide the obtained value by the tim interval to obtain the average velocity.

$\qquad\qquad \begin{aligned} \small \int_0^{10}x(t)&=\small \text{total distance}\\ \\ \small v_{avg}&=\small \frac{\text{total distance}}{(10-0)} \end{aligned}$

b)

• Just calculate the instantaneous velocities by substituting time values into the velocity function that is obtained by differentiating the distance function once with respect to time.

$\qquad\qquad \small v=\frac{dx(t)}{dt}\\ \qquad\qquad \small v(t=0)\,\&\,v(t=5)\\$