TutorMe homepage

SIGN IN

Start Free Trial

Carter K.

Aerospace Engineering Student at the University of Washington

Tutor Satisfaction Guarantee

Physics (Newtonian Mechanics)

TutorMe

Question:

A ball moves around a banked, circular track with a constant velocity of 2 m/s. The radius of the circular track is 0.5 m. Does the ball have an acceleration? If so, what is the value of this acceleration?

Carter K.

Answer:

Although the ball is moving with constant velocity, it does have a non-zero acceleration. Recall that velocity is a vector quantity. While the magnitude of the velocity is not changing, the direction of the vector is, and therefore the acceleration must be non-zero. For constant rotational motion, this acceleration is called centripetal acceleration. The direction of this acceleration is radially inwards towards the center of the circle. Calculation of $$a_r$$: $$a_r = \frac{v^2}{r} = \frac{2^2}{0.5} = 8 \frac{m}{s^2}$$

Calculus

TutorMe

Question:

The change in volume of a tub of water is given by the function $$f(t) = 4t + 2$$ $$(\frac{m^3}{s})$$. Calculate the mass of water in the tub after 30 seconds. Use a density of 1 $$\frac{kg}{m^3}$$ for water.

Carter K.

Answer:

The mass of the water can be calculated by multiplying the density times volume. Therefore, the change in mass is given by $$\rho*f(t)$$. To get the total change in mass, integrate this expression from 0 to 30 seconds. $$\int_{0}^{30} (1) * (4t +2) dt = (2t^2 + 2t) \Big|_0^{30} = [2*(30^2) + 2*30] - [2*(0^2) + 2*0]$$ $$\Rightarrow 2*900 + 60 = 1860$$ Therefore, the total mass of water in the tub after 30 seconds is 1860 kg

Algebra

TutorMe

Question:

A ball is thrown straight up from an initial height of zero meters with an initial velocity of 3 m/s. After what time will it hit the ground? Use g = 9.8 m/s^2

Carter K.

Answer:

Model the flight of the ball using a quadratic equation. $$ -\frac{1}{2}*g*t^2 + v_0*t + x_0 = \Delta y = 0$$ $$v_0 = 3$$ m/s $$x_0 = 0$$ m $$ -\frac{1}{2}*9.8*t^2 + 3t = 0$$ $$t*(-4.9t + 3) = 0$$ Solving for t, we get: $$t = 0$$ s, $$t = 0.61$$ s $$\Rightarrow$$ The ball is in the air for $$0.61$$ s

Send a message explaining your

needs and Carter will reply soon.

needs and Carter will reply soon.

Contact Carter

Ready now? Request a lesson.

Start Session

FAQs

What is a lesson?

A lesson is virtual lesson space on our platform where you and a tutor can communicate.
You'll have the option to communicate using video/audio as well as text chat.
You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.

How do I begin a lesson?

If the tutor is currently online, you can click the "Start Session" button above.
If they are offline, you can always send them a message to schedule a lesson.

Who are TutorMe tutors?

Many of our tutors are current college students or recent graduates of top-tier universities
like MIT, Harvard and USC.
TutorMe has thousands of top-quality tutors available to work with you.

Made in California

© 2019 TutorMe.com, Inc.