Help with physical science algebra? "A car is moving at 10 meters per second..."

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kinibee

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Help with physical science algebra? "A car is moving at 10 meters per second..."

Hi, I'm not sure which section this should be posted in since it is physical science homework, but it is mostly algebra. I'm not looking for answers but just how I should go about finding the formulas I need to use.

Here are the three problems:
17. A car is moving at 10 meters per second it begins to be celebrated at 2.5 meters per second squared. How long does the car take to reach a speed of 25 meters per second? How far does it go during this period?
35. A ball is thrown vertically upward with an initial speed of 30 meters per second. How long will it take the ball to reach the highest point in its path? How long will it take the ball to return to its starting place? What will the ball’s speed be there?
57. A parachutist whose total mass is 100 kilograms is falling at 50 meters per second when her parachute opens. Her speed drops to 6 meters per second in two seconds. What is the total Force her harness had to withstand? How many times the weight is this force?
 
Well, a good place to start is generally to carefully read the entire problem text and see what information you can parse from it.

kinibee said:
17. A car is moving at 10 meters per second it begins to be celebrated at 2.5 meters per second squared. How long does the car take to reach a speed of 25 meters per second? How far does it go during this period?
Click to expand...

First, I'll assume that you meant "accelerated" instead of "celebrated," as otherwise the problem makes no sense. The first step is to identify any variables we might need. I see that we'll need two variables to solve this problem - how fast the car is going (its velocity) and how far its moved (its position). Let \(\displaystyle v_t\) be the car's velocity after t seconds, and \(\displaystyle p_t\) be the position of the car after t seconds. You're given that the initial velocity is 10m/s and you can assume for simplicity's sake that the initial position is 0m. The next sentence tells you that the acceleration (change in velocity) is 2.5m/s^2. So, what's \(\displaystyle v_1\)? What's \(\displaystyle v_2\)? Can you create a general expression for \(\displaystyle v_t\)? Try answering the same questions for \(\displaystyle p_t\). What does all of that tell you about how you might solve the question?

kinibee said:
35. A ball is thrown vertically upward with an initial speed of 30 meters per second. How long will it take the ball to reach the highest point in its path? How long will it take the ball to return to its starting place? What will the ball’s speed be there?
Click to expand...

Again, we'll need two variables here - the velocity and the height. Let \(\displaystyle v_t\) be the ball's velocity after t seconds, and \(\displaystyle h_t\) be the height of the ball after t seconds. You're told that the initial velocity is 30m/s. Unlike problem 17, there's no given acceleration, but the ball will be fighting gravity, so it has a natural deceleration (i.e. it's slowing down). But how much is it slowing down by? What is the standard value used for gravity on Earth? At some point, the gravity will outpace the initial velocity of the ball, and it will begin to fall. But, what happens just before that? What does it mean, in terms of the velocity, for the ball to be at its highest point? Then, what does it mean, in terms of position, for the ball to have fallen back to its initial position? What will the velocity when that happens?

kinibee said:
57. A parachutist whose total mass is 100 kilograms is falling at 50 meters per second when her parachute opens. Her speed drops to 6 meters per second in two seconds. What is the total Force her harness had to withstand? How many times the weight is this force?
Click to expand...

Here, we'll need three variables - the velocity, acceleration, and force. Let \(\displaystyle v_t\) be the parachutist's velocity after t seconds, a be the acceleration, and F be the force. You're told that the initial velocity is 50m/s. To figure out acceleration, you need to factor in both gravity and the drag of the parachute. Combined, they slowed her down to just 6m/s after two seconds. If the drag is x m/s, can you create an equation and solve for x? Using that, what is the acceleration? The problem tells you her mass is 100kg. Now use the standard equation for force.

If you get stuck on any of these problems again, that's alright, but when you reply back, please include any and all work you've done on these problems, even the parts you know are wrong. Thank you.
 
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