Deriving Basic Physic Problem Using Calculus

Hypnos_16

1. Homework Statement

At a distance of 45 meters from a traffic light, a car traveling 15 m/s is brought to a stop at a constant deceleration

a) What is the value of Deceleration (-5m/s)
b) How far has the car moved when its speed has been reduced to 3 m/s
c) How many seconds would the car take to come to a full stop?

2. Homework Equations

I really want to solve this Physics based, but we need to use calculus to derive the equations. so there's no way of showing what equations i have used already

3. The Attempt at a Solution

I don't have an attempt at b and c because i don't know how to start them.
Help would be appreciated, it's the last two questions i have to do on an assignment for tomorrow. Please help

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dynamicsolo

Homework Helper
The acceleration function for the car is a(t) = -5 , a constant function. What are the velocity and position functions for this? (What is the relationship between a(t) and v(t)? between v(t) and x(t) ?

Hypnos_16

the relationship between a(t) and v(t), and v(t) and x(t) is that if you integrate a(t) you get v(t) and integrating v(t) gets x(t)

dynamicsolo

Homework Helper
the relationship between a(t) and v(t), and v(t) and x(t) is that if you integrate a(t) you get v(t) and integrating v(t) gets x(t)
Good! So $v(t) = \int a(t) dt = \int (-5) dt$ gives you...?

Hypnos_16

Well, from what i can tell, it give you the speed at any given time.
But if that's the case i don't have the time to solve B

dynamicsolo

Homework Helper
Well, from what i can tell, it give you the speed at any given time.
But if that's the case i don't have the time to solve B
You get an "arbitrary constant" from the integration. What you know from the statement of the problem is that when the car begins slowing down, which is at t = 0, the speed is v(0) = 15 m/sec. What does this make the constant from your velocity integral?

Hypnos_16

Acceleration???
Sorry, this really isn't clicking.

Ray Vickson

Homework Helper
Dearly Missed
1. Homework Statement

At a distance of 45 meters from a traffic light, a car traveling 15 m/s is brought to a stop at a constant deceleration

a) What is the value of Deceleration (-5m/s)
b) How far has the car moved when its speed has been reduced to 3 m/s
c) How many seconds would the car take to come to a full stop?

2. Homework Equations

I really want to solve this Physics based, but we need to use calculus to derive the equations. so there's no way of showing what equations i have used already

3. The Attempt at a Solution

I don't have an attempt at b and c because i don't know how to start them.
Help would be appreciated, it's the last two questions i have to do on an assignment for tomorrow. Please help
You might find it easier to consider the problem in reverse: starting from rest, a car undergoing constant acceleration reaches a speed of 15 m/s at a distance of 45 m.

RGV

dynamicsolo

Homework Helper
Acceleration???
Sorry, this really isn't clicking.
Are you asking about the "-5" ? Acceleration is any change in velocity, so slowing down is a negative acceleration (what people also called a "deceleration"). The calculations of motion can be done with positive or negative accelerations; the ability to work out the velocity and position functions does not depend on the sign of a(t).

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