Tutor profile: Alejandro C.

For equation 5x = 3, find x?

To find x, it helps if we could isolate it and have everything else on the other side of the equal sign (=). So how can we isolate it here? Let's move the 5, from the 5x, to other side. To move numbers from one side to the other, we have to perform the opposite function of the current function. So what's the current function in 5x, yes, it's multiplication. Opposite to multiplication is division. So yes, let's divide. And if you remember, what you do to one side, you do to the other. So if we divide both sides by 5, we get 5x/5 = 3/5. We know that a number over itself is 1, so in 5x/5, we get 1x, which could also just be written as x. Therefore, now we have x = 3/5.

A spring was at its resting position where it is attached to a wall at its left side and a block at its right side. The spring constant is k = 75 N/m. The block is moved rightwards and the spring's right end is displaced from the position of 0.200 m to 0.300 m where it is held in place. What is the spring force exerted on the block?

What are we given? (Spring Constant) k = 75 N/m and a displacement of 0.200 m to 0.300 m. What are our unknowns? (Spring Force) F = ? N What equations will we use? Force = - spring constant * displacement. Or F = -k *(delta) x Now, lets substitute our values into the variables. Let's first find (delta)x. (delta)x = final position - initial position (delta)x = 0.300 m - 0.200 m (delta)x = 0.100 m Now plug it all in the main formula and solve. F = -k * (delta)x F = - (75 N/m) * 0.100 m F = - 7.50 N Therefore, our force is 7.50N.

Suppose a ball is thrown upwards in a vertical direction only. At any point during the motion of the ball, what is the ball's acceleration, if it even has an acceleration?

Do you think the ball has an acceleration? If not, why not? If yes, we could look at the definition of acceleration, acceleration = (delta)Velocity / (delta)Time. So in other words, if any object changes velocity over a period of time, then it has acceleration. In this case, we know that usually if something goes up, it must come down. Through this process, we know that the ball's speed is not the same throughout the entire process (it slows down while it's going upward, then speeds up as it's coming down) therefore this shows that we have a change in speed or velocity over a period of time. This proves since there is a change in velocity over time, we have an acceleration. Once understood, now we ask what is the acceleration? if we don't know, let's ask ourselves what is pulling the ball down over time. Gravity, yes! Gravity on Earth has a constant acceleration of 9.81 m/s^2. As long as anything in this world (within the reasonable limits of constant gravitational effect) is in this world, it'll be constantly pulled down by gravity, or in this case, the gravitational constant. Therefore, because our object is being pulled by the gravity (gravitational constant) and we are neglecting other forces (such as drag force), then we can conclude that the ball's acceleration at any point is 9.81 m/s^2.