# Calculate (a) the average velocity of the particle

1. Sep 28, 2005

### juicev85

my professor gave us these two problems to try. I just started this physics class and am a little lost on these problems. any help/ hints would be greatly appreciated.

1) A particle moves along the x-axis according to the equation,
x(t)=50t + 10t^2(squared)
where t is measured in seconds and x is in meters. Calculate (a) the average velocity of the particle during the first 3.0 seconds of its motion, (b) the instantaneous velocity of the particle at t = 3 s, (c) the instantaneous acceleration at t = 3 s. (d) Graph the equation and indicate how the answer to (a) and (b) can be obtained from the plot. (e) While you are at it, graph velocity vs. time as well.

2) The starship enterprise returns from warp drive to ordinary space with a forward speed of 50 km/s. To the crew’s shocking surprise, a Klingon ship is 100 km directly ahead, traveling in the same direction at a measly 20 km/s. Without evasive action, the Enterprise will overtake and collide with the Klingons in just slightly over 3.0 s. The Enterprise’s computers react instantly to brake the ship. What acceleration does the Enterprise need to just barely avoid a collision with the Klingon ship? Assume the acceleration is constant.

Thanks.

2. Sep 28, 2005

### hotvette

Hints:

$$v(t) = \frac{d x(t)}{dt}$$

$$a(t) = \frac{d v(t)}{dt}$$

3. Sep 28, 2005

### Integral

Staff Emeritus
You are given a function of time which describes position of your particle. To find its location at any time t, you just evaluate your function at t. So at t=0 you have x(0)= 50(0)+10(0)2 = 0. You can find its position at any time in the same manner, you should be able to find its position at t=3.

What defining have you been given for average velocity? You know the position at t=0, you know the position at t=3 so you have a change in position and a change in time. You should be able to compute the average velocity.

I am assuming that this is a calculus based course, what is the definition of instantaneous velocity? Apply that to your position function, evaluate at t=3.

What is difficult about plotting functions?

4. Sep 28, 2005

### juicev85

thanks alot guys I solved the first question, oh and I didn't mean to include the last part of the first question (I can plot the function just fine). What about the second question, the star trek question. any ideas about that one?

5. Sep 28, 2005

### hotvette

Set up 2 separate equations of motion $$x_1(t)$$ and $$x_2(t)$$ (i.e. one for each ship), but use the same axis origin. What do you know about $$x_1$$ and $$x_2$$ at collision?