# calculus help

• Jun 27th 2008, 05:18 AM
tom555
calculus help
hi, i have some questions that i need help with i wondered if anyone could post the answers, here are the questions

1. The distance moved by a car is given by the equation s=3tsquared-5t+2 using differentiation find an equation for the gradient of the tangent to the curve when the time is 2 seconds ie differentiate and evaluate.

2. The velocity of a vibrating system can be modelled by the equation: v=5 sin 3t determine the equation for the rate of change of displacement with time (acceleration).
• Jun 27th 2008, 05:38 AM
TKHunny
I'm worried. These are the simplest possible applications of the derivative. I simply must question whether you have been paying attention in class. Perhaps you have been trying, but you have other distractions?

In the first, can you find ds/dt of s'(t) or whatever it may have been called in your class or your textbook?

You should get s'(t) = 6t - 5

Can you reproduce that? What shall we do with that to solve the problem as it is stated?

For the second, I have the same questions. Can you find dv/dt of v'(t) or whatever it may have been called in your class or your textbook?

You should get v'(t) = 15*cos(3t)

Can you reproduce that? What shall we do with that to solve the problem as it is stated?

Honestly, you're going to have to do better than tripping over these two problems if you are going to survive this course of study.
• Jun 27th 2008, 05:47 AM
nikhil
1)s=3t^2-5t+2
ds/dt=6t-5
6t-5 is equation for finding slope at time t.
at t =2
ds/dt=7
therfor slope at t=2 is 7
2) acceleration is given by dv/dt where v is velocity
since v=5sin3t therfor
dv/dt=15cos3t which is equation of acceleration
NOTE:acceleration is rate of change of velocity and velocity is rate of change of displacement.
• Jun 27th 2008, 06:17 AM
Simplicity
Quote:

Originally Posted by tom555
hi, i have some questions that i need help with i wondered if anyone could post the answers, here are the questions

1. The distance moved by a car is given by the equation s=3tsquared-5t+2 using differentiation find an equation for the gradient of the tangent to the curve when the time is 2 seconds ie differentiate and evaluate.

2. The velocity of a vibrating system can be modelled by the equation: v=5 sin 3t determine the equation for the rate of change of displacement with time (acceleration).

1.
$s=3t^2 - 5t + 2$
$\frac{\mathrm{d}s}{\mathrm{d}t} = 6t - 5$
You are told to find the gradient of the tangent at $t=2$ therefore:
$\frac{\mathrm{d}s}{\mathrm{d}t} = 6(2) - 5 = 7$

2.
$v = 5 \sin 3t$
$a = \frac{\mathrm{d}v}{\mathrm{d}t} = \frac{\mathrm{d}^2x}{\mathrm{d}t^2}$
$a = \frac{\mathrm{d}(5 \sin 3t)}{\mathrm{d}t} = 15 \cos 3t$