Try the fastest way to create flashcards
Question

The position of a car moving on a straight highway is given by

x=t2t390mx=t^2-\frac{t^3}{90} m

where t is the time in seconds. Determine (a) the distance traveled by the car before it comes to a stop; and (b) the maximum velocity reached by the car.

Solution

Verified
Answered 1 year ago
Answered 1 year ago
Step 1
1 of 8

In this problem, we are asked to find the distance traveled by car before it stops and the maximum velocity reached by car. To solve this problem, the first thing to do is to differentiate the equation with respect to time (t)(t) to find the x. Since the velocity is a rate of change of displacement with time and one way of expressing that is to say v=dxdt.v=\dfrac{d_x}{d_t}. We can use this to differentiate the position of the car.

dxdt=d(t2t390)dt=d(t2)dtd(t390)dt=2t3t290                (1)\begin{aligned} \dfrac{d_x}{d_t}&=\dfrac{d\Biggr(t^2-\dfrac{t^3}{90}\Biggr)}{d_t}\\\\ &=\dfrac{d(t^2)}{d_t}-\dfrac{d\Biggr(\dfrac{t^3}{90}\Biggr)}{d_t}\\\\ &=2t-\dfrac{3t^2}{90}&~~~~~~~~~~~~~~~~(1) \end{aligned}

Create a free account to view solutions

Create a free account to view solutions

Recommended textbook solutions

Fundamentals of Electric Circuits 6th Edition by Charles Alexander, Matthew Sadiku

Fundamentals of Electric Circuits

6th EditionISBN: 9780078028229 (2 more)Charles Alexander, Matthew Sadiku
2,120 solutions
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics 4th Edition by Randall D. Knight

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionISBN: 9780133942651 (8 more)Randall D. Knight
3,508 solutions
Advanced Engineering Mathematics 10th Edition by Erwin Kreyszig

Advanced Engineering Mathematics

10th EditionISBN: 9780470458365 (5 more)Erwin Kreyszig
4,134 solutions
Engineering Mechanics: Dynamics 3rd Edition by Andrew Pytel

Engineering Mechanics: Dynamics

3rd EditionISBN: 9780495295617Andrew Pytel
697 solutions

More related questions

1/4

1/7